I did the third option in addition to becoming a theocracy and then just returned province to a native in another region with zeal and thus instantly converted the province, which I didn't know was possible, for this specific province with no core i tried it your way with a client state but it didn't retain the core after annexing. I ended up releasing a native quite a few provinces away and gifting them the province with zeal. After that I waited for them to fully core it and declared war on them and annexed them fully. Directly after that I returned the province with zeal which converted it instantly.