Gorgon Gaze spell

I've been thinking of a spell that would essencially stun the target for a certain duration, perhaps doing damage overtime or damage instantaneous (or both). The thing is, I wanted to make it fancy, I wanted it to be the Gorgon Gaze (like, Medusa, turning you to stone). Thusly, I come across the question:

Is there a way that I can temporarily replace units' models within a trigger or within JASS? If not, is there a way I can perhaps cover units' models with models?

The idea here is that the unit is replaced/covered by a block of pure stone.

Thanks in advance!
-Mike.

Set the unit's transparency to 0% and make a really big rock model (using a dummy unit so you can change the scale) over it or something?

Or you can attach the rock model as SFX.

Another thing you might want to do is set the unit's animation speed to 0% for the duration in which it is stunned.