It looks like it wasn't my save file edits that caused my events to break. I've started another playthrough without amending anything and the cult stuff is still not working. I have my first election at the end of the week, so I'll update shortly on whether or not that is working now.
No, apparently the elections are still not working either. I haven't got as far as the amateur contests yet, but given the other two aren't working, it doesn't look promising. The only things that are changed from the base game in this playthrough are the user_config file, which doesn't have that many lines and I don't think has been changed since everything was last working other than maybe the addition of the line "init_worker_gender M". The only other things is deletion of many of the character images and duplication of others.