To sum up, you delete the offending directory and then run something to the effect of
git filter-branch --index-filter \
'git rm --cached --ignore-unmatch path/to/the/formerly/misbehaving/module'
I accidentally added another git repository to a git-svn repository, which makes it die when trying to push the changes. This technique helped me fix it. Documenting mostly so I remember when it happens again sometime.