I use git on Windows via cygwin and soon decided to use filemode=false (since otherwise I've got a lot of changes after the initial git clone). I'm definitely not interested in tracking permission at all, the only think I need is for some files to be executable. From time to time, I find that the x flag on some files gets lost and I strongly suppose it's because of git.
I'd be happy with a solution allowing to execute chmod a+x ... when needed.
I believe you want git update-index --chmod=+x <file>, followed by a commit.