This is a great job,
the comparison seem work perfect and calculation is very accurate, the guide is nice for all the sections you put in it and its certanly a kind of character i would play, as im between that people that love the melee of BS.
What i dont understand honestly is why sprit shroud over shadow Blade. Assuming you can use Booming Blade and SB on the same turn (with 2 swords or simply following this tweet from Jeremy Crawford
that seem totally allowing the use of BB even directly on the SB, at least RAI for sure, RAW im not totally sure but seem it work anyway, as "it counts as a simple melee weapon" refer already to everything) the damage looks better with a SB and you can even save highter spell slots, and while the speed reduction and the "no regain hp" is nice, you lost advantage in dim light that is better, especially if you often go in dungeons and still more as you want elven accuracy as feat.
Also i see, at least in my opinion, too many spells with concentration, while you dumped things like counterspel, synaptic static, steel wind strike, crown of stars (that give you a very nice use of your bonus action, and if you can apply Booming blade to SB directly fir sure its better than an offhand attack)) and soul cage that dont require it. I think you did it because with your INT you not gonna use that spells so much (even, for exemple, animate death or create undead for you is for sure better than conjure elemental because again, even elementals are much better than zombies, you ll see that elementals only sacryficing Sb or SS, while animate dead dont require concentration and you can use it even the day before for 3 walking zombie or skeletons shields, as well as, in my opinion, soul cage is certanly better than magic jar, especially for you with hight dex and low int. Magic jar is much more better for someone with hight int and lower dex, as it let you use the DEX, STR and CON of the new body, but it dont give you the WIS, CHA and INT of it, so you cant anyway bump int with it, while you can bump dex, and i anyway would prefer soul cage in both case, but i suppose you were "forced" to get it because you cant use tenser and soul cage together till very late), but at this point, its not better think to maximize INT over DEX? And i mean keeping being a melee focused character. With Triple advantage so often and no -5 penalty to hit for boost damage, i think you gonna hit as well with 16 DEX (or you can reach 18 if you really concern about it), and the 2 damage x hit its just nothing as you roll tons of d8 and just make 2 attacks. What you really lose is +2 AC while not bladesinging (but this get less important later on) and+2 initiative (this hurt a bit), but maximizing INT you bump also your concetration saves, so that after Resilient (con) you probably dont need also warcaster (till +15 to con saves its more than enough for kinda never fail it) and you can make space for other feat (being less tanky than the BS with blur, also mobile dont look so bad, also for trigging BB, but also +2 dex work as well, probabaly alert and lucky too) , plus it make you choose spells without concentration for debuff and great damage in the first turn (Ex: Bladesong + steel wind strike or synaptic static in the first turn, than second turn Bonus action Shadow Blade and full attack, or defensive spell as you feel), dumping many concentration spells that as you ll use often SB or SS would be there just for if one day you really gonna need. Yea, you probably lose a 5% hit chance and 2% pure melee damage if compared with an EK with same feats, but you miss anyway near to never plus you can make some good use (and kinda hight damage) of hight lv spells that require int (and that EK dream to can use one far day), especially in your first turn when you cant bladesong and cast shadow blade at same time, or some other spell can fill the bonus action that are not so busy with BS, also bcs in this character i think its really important to balance both the things he do, melee but also casting and even he ll focus more in melee mostly of time, there are some really powerfull combos in your first round that requires int and that help you a lot with your melee later on, steel wind strike make tons of damage bcs its against up to 5 creatures plus you teleport (if u get a fight with 5 creatures this make more than 150 damage plus you teleport and start Bladesong in the same turn! For me its absolutly a bladesinger spell, probably i consider it THE bladesinger spell), Synaptic static deal good damage to multiple targets plus it debuff them...do something like this while otherwise you have to cast mirror image on yourself and wait next turn for do anything else its for sure more useful, but also more thematic for a bladesinger, at least to my eyes.
I anyway want make sure that this is just an opinion, i didnt make any math about this except about SB being better than SS, so i dont actually know if prioritize int would work better or not on this kind of build, its just a feeling i have for better general sinergies, as im trying to build a similar character, but i thought to prioritize int also for dont need to choose too many concentration spells that fight with SB, and picking anyway spells that im gonna use often and with effectivenes. For concentration i only would choose SB, Hypnotic Pattern that have a good use even out of combat, Polimorph as heal spell for when im low hp and wall of force bcs its too good for think to dump this lol, total 4 spells (ok maybe this is really few

), while i see your build got around 18 of it (i think this is too much even for a common wizard, but maybe can be ok for them as they dont need SB or Tenser, so their slots and concentration are more free, but for your character i think it really mean almost never play many of that spells bcs mostly he ll choose tenser or SB for his concentration).
So, what i think is that probably giving up just a bit of effectivenes in melee (we are talking just about +1 damage for hit, +1 initiative and +1 to hit, maybe starting with 8 Str 16 dex, 16 int 10 Wis 8 Cha and 15 con or 16 from whenever you want add resilient (con), and so dumping warcaster for other asi, or you can even dump elven accuracy too and maximize both int and dex if you really feel that 20 dex is needed, but i still prefer 18 dex and triple advantage), you can synegize better with your spells list, and still keep being a character that stay 90% of times in melee having a huge general DPR and a very good melee dpr, howhever your is still a build that i would try and a character that i'd like to play. Bcs on this build, while i see the melee part working very well with everything calculated perfectly, lose something from the spells side that probably can sinergize better with each other making different choices, plus some spell you choosed that i really would totally dump, but that's personal flavour i suppose.
PS Normally i dont like Tenser Transformation (even on this build it work better, especially if you cant use booming blade directly on the SB) as you lose shield and absorb elements (also counterspell if you have hight int and if you are the one in your party casting it, this can be a huge problem) and the damage is just same a SB of 5th lv, so also for focus on melee i feel its not so necessary to get Tenser transformation. 50 HP is really nice, better advantage than shadow blade too even you can get it from other source, but the highter lv slot use its really bad (you have only one 6th lv slot for very long) and everything get worst when you read: "you cant cast spells"...maybe can work better at lv 13 when you get simulacrum, but i still prefer SB with my best friends (shield and absorb elements) that never betray me, also bcs with that 6 lv slot i can cast soul cage (6 uses it mean at least one entire fight, so same tenser, as a fight i think normally have 4/5 rounds, or even less, while you have advantage on almost anything you want, not only attacks roll, depending on the situation. If nothing happen you just get your advantage on attack roll at your turn and with your bonus action use the soul cage again, but if you have to roll a save during the turn, for sure you gonna use it on the saving, making it appealing to me more than tenser, plus it have some out of combat uses and anyway SB can cover Tenser dpr, plus you still can cast your reactions...except you found some very good sword, which normally dont happen to me lol, as you should find a shortsword flametongue for exemple, and when the DM put something like this in play its often a long sword for the fighter or paladin, still worst if you get a rapier as proficiency as there are no good magic rapiers, i would not bother with tenser, also because if you find a good sword applying to it you can always add it later on, or find a scroll for copy the spell, for a sort of magic berserking lol, that also thematically would be nice) or true seeing (in some circustances its very useful, but there's no way to be wrong with it). For Fireshield im not sure, as you are supposed to not get hitted, but i think you want use it with tenser transformation so in this case have its good reason, but its anyway other action casting, after the first turn where you have to cast tenser and badesong together, it can work anyway but it make you do nothing for 2 turns, probably its better hit with tenser than cast it, except you find a way for precast it no more than 9 minutes before the fight, good anyway because it dont burn your concentration. Darkness i also dont like it, is concentration plus you can see inside there...but your party no, more usefull with a ranged wizard, not if you want go in melee, or well, less useful for sure and risky. Resilient sphere is not bad but i see many wizard stay there and do nothing bcs of it, double face spell + have concetration. Animate object its a good damage spell, but you use your swords for damage single targets not teaspoons, can be good for protect your group while you are running away but, for the style you want play, i dont see any other reason for cast it and lose tenser or SB. Reverse Gravity have concentration but is much more situational and you can make good use of it when its necessary, so it is ok for me. Invisibility at will ok, its nice...but you can use it anyway once for time, i would push that "unlimited" on misty step. Counterspell with int so low also dont convince me totally, probably better leave it to someone else, or prioritize int, except you are ready to expend always your higher spell slot for it, but once you gonna roll for it, you probably gonna miss kinda often on mid/hight lv spells. Shadow Blade for me its better, but anyway i think you should choose only one between SB and Spirit Shroud. As cantrip i strongly recomend shocking grasp (better with hight int honestly, but even its a spell attack its good also with your low int, as it have advantage if they are wearing metal), for a BS with decent int its for sure better than true strike and blade ward, for you im not sure honestly, as mindsliver also con be useful sometime (but only if you have a decent int, so probably not in your build)