I am 99% positive I know which professor this is and if it is indeed her, I'm sure this is precisely the case, haha.
I went ahead and splurged on Interfolio (since almost all of my apps accepted it) and it was definitely worth it. Having control over my recs helped me breathe a lot easier.
I am so sorry, bfat, that Michigan is being so rigid about the rec. What I find so frustrating about this is that one of recommenders told me (re: why I should e-mail profs I'm interested in where I'm applying, introducing myself) is that, realistically, it's unlikely that most committees will even touch the pile of apps until late January, as there are hirings to take care of first.