First, what i WOULDN'T DO:
1. Don't get rid of twitching, the game will be worse for it, this isn't wow and noone wants it to be.
2. Don't get rid of the attack sequence, this is how TWF paladins twitch and it is awesome and fun.
What I would do:
firstly, to get rid of lag:
1. yes, remove physics checks for second and third strikes and just use the first strike to see whether they all hit or miss.
2. yes, remove some "attack speed boosts" and replace them with "double strike" i can see that for DPS lag, this might be effective
melee balancing:
1 simple melee balance fix:
get rid of stupid weapon base damages and crit ranges!
a longsword should do 1d8 damage, it doesn't matter if its epic of muppet slaying or whatever, it is still a 1d8 weapon because it is shaped like a longsword. It is such an affront to me having played pen and paper to have my perceptions of the what a longsword is by messing around with the base damages of weapons.
No exceptions, no rainchecks.
further thoughts.
Problem: armour needs to be useful past level 10, its just silly that 90% of characters (or even 95%) don't bother wearing armour, its ... plain wrong.
Possible solution: well umm, ok, im a bit stuck here. It does seem however that the basic D&D mechanic breaks down in this scenario where there is vastly varying AC numbers and it would seem that a new mechanic needs to be brought in to provide a solution. I'm not sure where the inspiration for that mechanic might come from. Maybe glancing blows need to hurt more, and the amount that they hurt is based on the heaviness of your armour. Break up glancing blows to say that if you would be hit my a melee touch attack then you take a glancing blow which is mitigated by L/M/H armour at rates of 25%/50%/75%. This would have to happen even if the guy is hitting you normally.