The list of spells that synergize with Bladechanter/Eldritch Archer seems very small if we're not expected to use spells from the PHB. Wizards have very few single target/touch options in their spell list. So far the only spells I can see that you can use are the following:
1st:
Charm Person (Though, arguably, you're damaging the target in the same action that you're charming it, doesn't that break the effect?)
Magic Missile (as long as you only target the one creature you're hitting, best/only option imho)
Corpse Explosion (Eldritch Archer only - the spell already auto-targets, you give up an attack for some action economy and range perhaps)
2nd:
Acid Arrow (Perfect example, though only marginally better than magic missile)
Blindness
Enlarge/Reduce
Ray of Enfeeblement
3rd:
Bestow Curse
Haste
It feels like the big payoff for delaying extra attack for 5 levels is being able to, essentially, cast magic missile along with one of your attacks (and depending on what you're fighting elemental arrows can double your damage, or just be a neat special effect). Arrow Enchanter then becomes essentially just bonus accuracy option, as magic missile [3d4+3(10)/1d4+1(3) per SL) is superior to 2d6(7)/1d6(3) per SL. Also, once you get signature spell at 5th level in Wizard, magic missile doesn't even cost a spell slot, and is equivalent to using Arrow Enchanter and burning a 2nd level slot.
I'd be open to other opinions/interpretations. I still think the synergy tree is worth it, though I suspect it's not necessarily mechanically optimized (which is fine)
1st:
Charm Person (Though, arguably, you're damaging the target in the same action that you're charming it, doesn't that break the effect?)
Magic Missile (as long as you only target the one creature you're hitting, best/only option imho)
Corpse Explosion (Eldritch Archer only - the spell already auto-targets, you give up an attack for some action economy and range perhaps)
2nd:
Acid Arrow (Perfect example, though only marginally better than magic missile)
Blindness
Enlarge/Reduce
Ray of Enfeeblement
3rd:
Bestow Curse
Haste
It feels like the big payoff for delaying extra attack for 5 levels is being able to, essentially, cast magic missile along with one of your attacks (and depending on what you're fighting elemental arrows can double your damage, or just be a neat special effect). Arrow Enchanter then becomes essentially just bonus accuracy option, as magic missile [3d4+3(10)/1d4+1(3) per SL) is superior to 2d6(7)/1d6(3) per SL. Also, once you get signature spell at 5th level in Wizard, magic missile doesn't even cost a spell slot, and is equivalent to using Arrow Enchanter and burning a 2nd level slot.
I'd be open to other opinions/interpretations. I still think the synergy tree is worth it, though I suspect it's not necessarily mechanically optimized (which is fine)