Yea, this is more of a list of possible criteria to hit, not really a proposal yet.
I'm still debating. I'm starting to go back to the beginning of this discussion, and I'm thinking that there should be some baked in scaling in the base rule, no style or feat required. Turn the fighting style into a small damage bonus (like Dueling), and use the DW feat to enable the BA attack (to parallel PAM and XBE). Add in a feat to allow one-handed weapon damage to scale, much like GWM. This would benefit both DWers and SnBers.
The "followup attack on a miss" concept might be a good concept for the base rule. Less max damage than a 2H weapon, but more consistency.
Honestly, I was getting ready to fight and then what you said seems really interesting.
2d6+3 at 65% hit is 6.85 with crit. 1d6+3, reroll miss (without ability mod) at 65% hit would be 5.2575 with crits. Leaving the ability modifier on would up it to 5.94, which is still lower than great weapon but not significantly so. It fits into an image of TWFing that I think people can get behind. I'd allow default to just attack two separate targets for 1d6+3 instead.
Style could allow for use of non-light weapons.
Feat could grant a bonus action attack and an AC boost.
I'm not sure I'd want a separate one-handed weapon feat for -5 to hit/+10 damage. I'd like to leave that in the hands of the two-handers (light crossbows are two-handed since you need a loading hand still). I'd like one-handed weapon wielders (sword and board and TWFers) to have a different feat they pick up for that.
The rogue would gain big here, so we'd want to address that. The monk may gain too.
I kind of like this. It's different from just having TWFing deal equal damage with GWFing, and it avoids stacking issues with on-hit effects (it still favors once per turn on hit effects, since you have more chances for it to proc, but those gains drop rapidly once you have 2 attacks: 65 for one attack goes to 87.5 for two goes to 95.6 for three.
Would you let them get this reroll for each attack from extra attack? I'd say yes. It kind of works like psudo advantage (but doesn't stack well with advantage). I'd even suggest players roll 2d20 and pick the highest, but that would enable critfishing.