That's exactly how we solved that problem. Simply create a throw-reaction move for small, normal and tall characters. From this animations you could also create an override for the attacking character to create different heights depending on the size of the opponent. You can do a lot of stuff with character-specific moves.

You can specify a character (name) directly to the animations:

You also have to assign the different animations to the movelist of the characters.

Hmm. Sorry I can't follow. I think I don't understand your problem. Maybe you can give an example, what exactly you have problems with.

Ok, I would try this:

You create a normal throw-attempt animation, then create three different throw-confirm animations. Lets say they are 100 frames long and identical from frame 0-20. The jump starts at frame 20, so the animations are different because of the jump-height. Create one throw reaction animation.

Now create the move-files. You need one throw-attempt and three throw reaction moves (small, normal, tall). Assign the reaction-animation to all of those. Then create a throw-attempt-move with one of the three animations. At frame 20 create an opponent override. For each possible opponent create an entry in the character-specific override-settings: enter the characters name and choose reaction/small  reaction/normal or reaction/tall.

Create the three throw-confirm move-files (use animation from 20-100) for a small, normal and tall character. Create an opponent override in the reaction/small-move frame 0 to throw-confirm/small-move (0 which is 20 in the complete animation) etc.

It's very easy but hard to explain