You can get git log
to show you just the commits that actually changed a particular file, and you can use its "pretty" output formatting to spit commands to do anything you like. So with a bit of shell-variable munging added in,
git ls-files render | while read f; do
git log --pretty="git show %H:$f >${f%.*}_%at.${f##*.}" -- $f
done | less # sh -x
The above numbers the files with their modification timestamp rather than a serial number, if that's too much for your client then you can get the shell to serialize them for you with
git ls-files render | while read f; do
git log --reverse \
--pretty="git show %H:$f >${f%.*}_\$((1000+++x)).${f##*.}" -- $f
done | less # sh -x