Disclaimer: I never did anything with an s3 mini, nor did I read this whole thread that carefully. It’s late.
2 thoughts:
1. Did you try CM11 without gapps to see if it runs first? That would be my first process of elimination when troubleshooting.
2. I’ve had similar ROM problems with samsung htc and other phones which involved having outdated (or too new) firmware (especially the radio version) or the wrong kernel. Just be careful. Messing with firmware could brick things and you can lock things that you don’t intend to.
I’m done here. Good night.