To me this comes down to legal. If the person has been documented as a problem, corrective actions have been documented, and whatever you have as an HR dept says it's ok to fire the guy, fire him. If you feel guilty, then offer him a portion of his potential vesting, and explain that he was shit, but you don't want to leave him empty handed.
Is the timing great? No. That's why it must be well documented the behavior your penalizing. He will almost certainly come back to sue you for wrongful termination if there is no documentation (and you have any value to your shares).
Is the timing great? No. That's why it must be well documented the behavior your penalizing. He will almost certainly come back to sue you for wrongful termination if there is no documentation (and you have any value to your shares).
Good luck, cut the dead weight, and move on.