D&D is an RPG. A Role playing game. Characters play a role in a story. The game is at its best when we tell a good story. This sounds like something very cinematic and dynamic - a good story.
D&D is also a game, and games have rules and balance considerations. So, if a creative player comes up with a creative way to be more effective, the story needs to have a creative offset.
The way I would rule it: You're aiming for split second timing, whether you are casting a spell or pulling out of a dive. If you're off, you either kill your momentum and throw off your strike by pulling out early, or you hit ground by pulling out late.
You can attempt a Dexterity (Arcana) check for Feather Fall timing or Dexterity (Acrobatics) for pulling up when flying (as dexterity is the ability for split second timing). The DC would be set by the distance you fall: (12+1 for every 10 feet you fall).
If you fail, you are too late and take damage for falling. Roll a d20 and add your proficiency modifier. If that exceeds the AC of the target, it also takes the falling damage as you land on it.
If you succeed, but do so by only up to (1 per 10 feet fallen), you pull out early and either lose the attack (if flying/using acrobatics) or feather fall down to the enemy and get to make a normal attack when you fall to them. You stop early by 10 feet per point over the DC you get. Count the feather fall distance against your movement available that turn.
If you succeed by (1 per 10 feet fallen) or more, you get to add 1d1 per 10 feet of damage fallen to your damage to your attack role and crit on a 19 (if you hit) or 20.
You must make a strength saving throw, SC 15, to maintain your grip on your weapon if you hit the ground or hit the target.
So, as an example: You are 30 feet up and attempt to dive and use feather fall to halt your momentum right before after you hit the target, but before you hit the ground.
Your DC is 12+3 = 15 for Dexterity (arcana).
If you roll a 14 or less, you make a d20+proficiency roll to see if you land on the target. If so, you both take 3d6 falling damage. If you miss, only you take it.
If you roll 16, 17, or 18 you will cast the feather fall 10, 20 or 30 feet early, respectively. You'd feather fall down and could make a normal attack.
If you get a 15 or if you get a (19 check or above) on the check, you'd get to add 3 to the damage.
If you roll a natural 19 or 20, you get to deal a critical hit. As the +3 damage were d1s, they are doubled on the critical.