2) Allow finishing off knocked out enemies with melee weapons the same way you can heal them with bandages/medikits. If there's no one in front of you, then let the game check if there's someone below and perform an attack vs them. Or add 0-range "ranged" attack to melee weapons called "finishing blow" which can only target the same tile as the user and thus only attack below. It's especially vital for Monster Hunter condemnation, which is great to offset -HP from the Lawyer. As you need to kill the beast with melee weapon and blood hounds are apparently bandits (lol), it sometimes have the reverse effect and adds to the Lawyer instead of Monster Hunter, if blood hound survives and collapses. As the result you need to carry ranged weapon to finish off blood hound or wait for it to bleed out just to avoid really bad punishing condemnation.
This would sadly interfere with a different OXCE mechanic. If you are standing in front of a barrier, you can attack it in melee. If you could also melee units lying under your feet, it could get unclear whether you want to attack a wall in front of you, or a Blood Hound under your feet.
There used to be a Coup-de-Grace mechanic, but it was removed because it allowed any melee weapon to finish off any fallen unit. (even such as a charm dealing weapon to a robot)
But mostly, I'd suggest just doing a fix to condemnation triggers.
What I mean is, for knockdown and kill condemnations, only final state of the unit should count, and only the final tool that affected them.
By doing that, if you slash a Blood Hound with a sword, it falls over and dies a few turns later, it should count as kill with sword, but not a knockdown with sword.
If you slash a Blood Hound, then heal it's critical wounds with a Bandage, it should count as knockdown with bandage.
This would also prevent players from farming an absurd amount of knockdowns on a single enemy by repeatedly knocking them down with a guaranteed non-lethal weapon (such as a cattle prod), then reviving them.