First, once again, the styles don't affect your weapon and armor proficiencies. You could just as easily play a duelist in plate armor with a greatsword, negating that difference in raw damage. In actual play, the fix here will involve a decent specialty for swashbuckler types, which I agree is needed, not changes to the fighter style.
I used the standard packages and flavor outlined in the playtest for each fighting style. Duelist implies specific flavor traits - Light armor, High Dex, Finesse Weapon. Slayer implies specific flavor traits - Heavy armor, High Str, 2H Weapon. A "duelist" in plate armor and a greatsword is a "slayer." A "slayer" may be a great swordsman and win duels...but that doesn't make him a "duelist" anymore than a Nissan GTR engine in a Juke makes the Juke a GTR. There are a lot of other trim/spec considerations beyond horsepower that dictate performance metrics and how something gets around a track.
Second, what specifically makes you dismiss the utility of tumble and shift? Shift lets you attack an enemy 40 feet away, and tumble lets you move through enemy squares.
Tumble and Shift came in useful in the final fight but that was primarily due to the inducing of status effects by the Wizard onto the Giant. Truth be told, the unit would have been better served with another archer instead of a "duelist" in that scenario. The archer could have maxed out damage with Deadly Strike without ever being at risk of being hit and thus subtracting from the unit's efficiency within the Action Economy (forcing the cleric to heal rather than do damage). If the Duelist had a rider to its attacks which applied a negative status effect to an enemy or upped its damage to "striker levels" to where the Slayer is and then used its mobility to get itself out of danger or up its defenses...then it would be doing something of worth to positively affect the unit's Action Economy relative to its enemies' Action Economy. As is, Tumble and Shift are extreme corner cases to avoid Reach AoO by large creatures and to attempt to use blocking terrain/difficult terrain to kite enemies. I really, really tried to leverage and test Tumble and Shift with all manner of terrain elements, an Artillery and Brute (with AoE reach) in the last battle. It just doesn't pan out all that well and again, the damage of a "duelist" which is supposed to be a "striker" is pathetic. Worse, yet it does its horrible damage while inflicting no rider effects on enemies nor upping its AC/Dex save through its mobility. As is, the Duelist reminds me of the 4e Rogue/Scoundrel Duelist build with the feature "Artful Dodger"...but without Sneak Attack, Sly Flourish, and 2[W] and 3[W] attacks that grant the Duelist large shifts and passive AC and Dex modifiers until the end of its next turn. The Slayer at least feels like and performs in-line with the 4e Great Weapon counterpart with cleave and high relative base damage.
Another question on that sample combat: how could Glancing Blow have been useful? What were the ACs of the monsters you were using? My understanding is that nothing in the playtest bestiary has an AC over 16 or 17 (and only a couple level 5 elites have that), rendering Glancing Blow almost completely useless. (Are you house-ruling it in some way so that it triggers on any miss, or on a miss of 5 or higher?)
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Another point to consider: the Slayer's extra damage from Cleave is going to be largely against mooks and possibly normal enemies, while the Duelist's improved mobility could ideally allow him to be gunning for mages and other valuable targets hiding behind enemy lines. Both roles are valuable in combat, but their relative value to the party would depend on your teammates: for example, a party with a wizard or (even better IMO) a draconic sorcerer would have less need for additional minion mop-up, while a party with a rogue or archer would have less need for additional targeted damage.
First things first. I am not at home so I don't have my playtest material or my excel so I'm doing this off memory. However, I will defer to you as I'm sure you're correct on Glancing Blow. I was using it incorrectly. I just assumed it worked as the "Reaper" Feat and that you spent a CS die on "any miss" to do that die worth of damage to the missed target. With bounded accuracy and AC, that stipulation of "a miss on a 10 or better" is flat out awful. Its not quite as bad as Elves not being able to Finesse Long Swords (and thus presupposing Strength for Elves as primary stat...or a worthless infantry that cannot hit the broad side of the barn) but it is quite bad. That must be changed in the next iteration (either to lose the prereq entirely or change it to 5 as you mentioned). That being said, it triggered a few times per fight (maybe 6 total) probably for somewhere around 25 damage so it isn't an enormous difference but it puts the percentages closer together (they are still horribly disparate as allegedly comparative striker builds).
Cleave, on the other hand, was enormously useful. I didn't use it at all in fight 3, but I believe I received an average of something like ~ 3.7 free MBAs (about 40ish gross damage) per series of 3 tests due to Cleave. The augment to damage (in a large infantry oriented fight), and thus relative Action Economy, is considerable.
See above for my thoughts on Tumble and Shift.
FYI, in my tests I upped all HPs (except for minions) dramatically. I wanted them to be HP bags as I wanted to get a large sample of damage/character without having to run an inordinate number of new combats. I basically used templates of the monsters in the bestiary and scaled up their HPs and used all of the other main stats. Only in the "Boss Fight (3)" did I create my own creature. I basically made a 120 HP Hill Giant with Reach (to attempt to leverage Tumble a bit for kiting with Ray of Frost and to get back into melee when knocked back without provoking an AoO), a knockback on a hit, an 18 AC (buffed to 20 by an Ogre Shaman - modeled after a Dark Priest), modeled generally after the Ogre.
Test 1 - This fight used 8 (4 HP, 15 AC) minions and a leader (modeled after hobgoblin) buffed to 70 HPs (17 AC), .
Test 2 - This fight used 3 (35 HP, 16 AC) guards (modeled after orcs) with a (70 HP, 16 AC) leader (modeled after an orc leader).
Test 3 - 120 HP, 20 AC (with SoF) "Giant" and 60 HP, 16 AC "Ogre Shaman" as outlined above.
Again, see the Soundrel Duelist/Fighter Brawler/Bladesinger for ways to make the 1H finesse weapon, light armored skirmisher striker relevant compared to his companions. You need to add damage riders (to at least make up for comparatively poor median weapon damage), action denial riders or negative status effect riders (to provide the flavor of tactical mobility that actually affects the Action Economy), Defense bonus riders (to make up for lack of shield) in order to make them relevant. Without 2-3 of those, their inherent weaknesses handicap the build to irrelevancy.
Another option to help address this problem would be an Encumbrance system that worked just a little harder at game play and a little less at simulation. (And it's not as if any of the previous systems have been poor on this issue. So we are talking a slight shift.)
To wit, imagine a simple Encumbrance system that readily lets each character carry what they need to do their combat job, and then leaves excess capacity for other equipment. Then provide other equipment that significant strategic capability, with the main cost being weight not gold, and some of it being consumable. The fighter, usually being the strongest, will be able to carry more, and more variety.
It would be necessary to not go so gaga with armor and weapon weights, so that excess carrying capacity will tend to favor the stronger characters. Then the strategic equipment needs to be heavy enough to limit how much characters can carry. If some of this equipment is magical, that's fine too. Just make it light and cheap enough to use, but heavy enough that the 8 Str Wizard can't load up a lot of it. Bags of holding and other such options will also need tweaking.
Some groups will use such a system to gravitate towards the fighter carrying backup food and ammo for other characters, so that their characters can have more of this good stuff, but that's a playstyle choice and can be addressed in advice. So tweaking Encumbrance is not a complete solution. However, if you want to make "strong guy" matter in a strategic sense, then you need an Encumbrance system that supports this, but is simple enough that people won't ignore it in frustration.
I would love a very easy to use Encumbrance system and I can see how this would help the Fighter have a Batmanesque Strategic Exploration Niche as "tool-guy". I would love to see that but again (as you stress in both posts) it would need to be easily applicable and as non-fiddly as possible. However, I too share ZRN's concern with the ability to exploit useful, burdensome tools by way of summoned "mule minions" and bags of holding. I would think that that could be worked around. You could keep these tools "Fighter-specific" by either having high Str prereqs for use or demand a difficult Str Ability Check in order to use. Conversely, you could give them a "Tools of the Trade" skill whereby they are the only class with the bonus and each of these tools require a Skill Check/Ab check to use.
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Manbearcat , I think your secondary backgrounds for fighters (sailor, soldier, etc) make some sense, but could potentially get a bit too complex. Maybe something like the following:
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That looks good to me. So long as Fighters can legitimately, consistently involve themselves in Conflict Resolution within the Exploration and Social Pillar (within the scope of their martial flavor) I'll be happy, regardless of how its actualized.
