Move rangehood fan inline
Grease isn't any more of a concern than it is now if the existing traps remain in place. If it was, the original fan would also be in jeopardy. 

Airflow isn't really a concern, either. The original fan can probably be easily removed (and the new one connected to its power supply). Even if it can't, it won't reduce flow much, especially if it spins passively. 

There's no need for a super-turbo-jet-fan. Anything that claims to move as much air as the original is suitable, and the fact that it's remote should significantly reduce noise.

I'm with you on the noise thing. I don't understand why remote fans aren't the default. My new "low sones" bath fan buzzes like a chainsaw half the time. 

Go for it.