Is this a stupid idea, or are there straightforward ways to make it work?
Ideally I'd like to stop using fedora template altogether, to get one less thing to be backed up. However it's not important enough to put a lot of work into making that happen.
Check this article - https://www.qubes-os.org/doc/templates/minimal/ (scroll down untill you see "Debian" header)It explains what you need to install so that debian template will work as expected.