Thanks for the points!
"Monks can TWF and still use martial arts."
Monks need to be dealing 1d8+3 +1d4+3 to keep up with sneak attack damage (3d6+3 is 13.5, monk is 13). Reword their martial arts. They get +1 attack always that has to be unarmed. Flurry is a bonus action for another +1 attack that has to be unarmed. Martial Arts is an upgraded TWFing basically. I'll have to circle back to decide what happens at level 5 for the Monk.
"Any magic items that grant a per attack damage bonus start to greatly favor the TWF."
Other than magic weapons, which I addressed in my original post (2 magic weapons for the TWFer can be compared to 1 magic weapon and a belt of giant strength for the GWFer), is there anything that grants a blanket bonus to all damage? I'm not aware, but it's been a while since I read all the magic items and I haven't ever fully digested them.
"Haste would grant 2 attacks (possibly is intentional)"
Like you said, this is fine, it lines up with Greatsword.
"Gloomstalker would potentially get a bonus action attack on first turn as well with his ability."
What bonus action attack would you be looking at there? Or do you just mean from multiclassing?
"Crit Fishining on Paladins or warlocks could be very strong."
The fix here is simple: base smite is a bonus action. It's basically a raw smite spell that you automatically know. I don't like smites being able to be stacked or multiple smites in a round. I'd prefer they get paced out, and once per round would be fine. Now you have to hope your first attack is a crit.
"Valor bards feel better as dual wielders."
At least they'd have options between sword/board, great weapon, or two weapons.
"Samauri's can actually TWF and use their Samauri ability"
Yeah that would be nice.