I don't think you understand what Crow Form is used for and why it is an essential part of making units appear to fly. You never actually have to have the unit
use the crow form ability, just add/remove it so you can set the unit's fly height with triggers.
I still really do not understand what you want to do to the targeted unit (maybe explain step by step: 1. units is raised up in the air, 2. unit is turned into X, 3...), but it sounds like you want to elevate it and morph it into one of 5 different units temporarily for the duration of the raise. There are better ways of doing this to achieve the same visual effect without actually having to transform the unit into something else, but if you insist on actually morphing the unit into something else, you should use bearform, not raven form:
Hero passive transformation
There's no easy way to 'remember' what the unit's unit-type was before you morph it in the way that tutorial shows or using Chaos that doesn't involve hashtables if you want it to be MUI... and as far as I know there's no way to morph an arbitrary base unit into a specific other unit and then back again later
without using Chaos or the method in that tutorial. The way I see it you probably have to use that method with a bunch of different versions of the spell to morph into the right unit. Perhaps you could use a very short duration Metamorphosis to do it, and maybe Tinker's ultimate can have a duration but IDK. Better explanation might make it easier to suggest what to do.