The floaty feeling is a simple issue caused by years of complacency.
The only game I've played with satisfying first person melee is FEAR, and that's because they go to great lengths to make the player not feel like a disembodied floating camera. You have to ditch the traditional vmodel/world model first person implementation, or at least try to alleviate that by having the floating disembodied camera track the world model animation of your character as you do your attacks.
It feels slightly stocky and not as fluid having the camera move in ways that aren't 1 to 1 with the keys pressed (camera bobing back and forth as you walk, camera bobbing to the side as you punch because of your shoulders rolling), but it gives the impression of actually throwing your weight into attacks, rather than just swinging your arms like an autist playing fisticuffs in school. This is also very important for getting the attacks from the player perspective to accurately represent what is happening in the game world, without this kind of camera shifting, its straight up impossible for an attack as it exists in the world, to end up looking the same as what the player sees, and that's how you end up with npcs ragdolling incorrectly and force being applied in confusing ways.
For unresponsiveness, it's actually a similar issue, if the windup of your melee attack happens offscreen (which there has to be, you can't swing a sword without drawing it back), there's necessarily going to be at least one frame where it seems nothing is happening because your weapon and arm are offscreen, camera shifting helps portray that your character is shifting his weight and not just waiting a few frames to do what you asked him to. It all just comes down to giving feedback to the player which represents what is really happening in your game world. If he's holding his sword down at waist level, then don't show an animation of him holding his sword up to his face like he's trying to check his teeth in the reflection of his blade.