I have very little personal knowledge of FOIA, and this is written assuming that you know have no personal experience with it (so if you do, I suspect this will read as condescending, which is not my intent). I suspect that short of hiring / recruiting a politically influential person (relevant to UMich) to help, this is all the useful advise available (for better or worse).

Beware administrative (search) costs and copying costs.

Try to describe the data you want in a way that (a) makes it easy for the searcher to determine if something is responsive to your request, and (b) makes it seem like finding the documents will be really easy for some mindless bureaucrat to find. In writing the request, assume the professor will never personally do anything to grant the request, and a grad student might spend 5 minutes pointing towards a filing cabinet.

Additionally, politeness and clarity are under-rated virtues in the practical invocation of legal rights.

Hi. This is a FOIA request for X. Thanks for your help.

That's a good template for the first draft of the FOIA letter.