You could write a custom system for tagging certain content to git commits using git notes and then write a batch script to fetch those files from some other service based on your current local head. Of course then the system you pull from would need to have versioning which at that point you are back at perforce/svn etc. If you don’t care about versioning your content then yeah, you could map dropbox/google drive to your content folder. You would lose versioning and dropbox/google drive both charge monthly fees for large amounts of data.
So I guess what I’m saying is if I were you, I’d just stick with perforce. You are most likely going to have to pay no matter what, it might as well be for more perforce space.