What you could do is remove the "Catholic" tag entirely, assigning it to no one. Then give all Christians, orthodox and catholic, the "Muslim" tag, call them "christian". Assign all muslims the "orthodox" tag. Then you have religious enemies between the two, pretty regular gameplay. Plus the Orthodox/Catholic divide is less important when playing a Muslim country. If you wanted to do a bunch of work, you could use the user_defined traits to give Catholic or Orthodox in a similar way the Shiite and Sunni traits are given, but its probably unnecessary.
Don't use the PAPA tag (too much hardcoded stuff), just give the Papacy a different one and add events that will respawn that tag as well as force its law to elective, though I'm not sure if there's a way to force a country to spawn as a bishopric. In some sense this would be more realistic, as the papacy would be led in Roma by Italians primarily, instead of the weird mix of cultures it is currently. If it got conquered though, it would respawn as a feudal form of government rather than ecclesiastical, I think. (In fact I'm not even sure the Muslim tag supports ecclesiastical government)
Also something that sort of bothered me when I was doing it was bishoprics. As far as I know, Islamic society didn't have anything similar to bishoprics. I'm pretty sure you'd have to mod the exe to prevent the ai from making them, not to mention the player. Though I actually don't know under what circumstances and using what criteria the orthodox ai creates bishoprics. Are bishoprics even appropriate for the orthodox religion in vanilla?
ALSO (!) how exactly to define the Kingdoms for a Muslim mod seems questionable to me. Many islamic empires were known for their leading dynasty (Seljuks, Ottomans, Mamelukes, Fatimids, Zirids, Al-Murabitids, etc) I can only think of a few (actually one at this moment - Rum) that were named for a geographic area. Did the former empires have names they called themselves after the area they held, that Western history has just neglected? Or is that what they called themselves, in that case, it seems Muslim gameplay would be underwhelming. (You'd never be able to form the Mamlukes for example, just Al-Misr [Egypt]; you couldn't form the Ottomans but you could form Rum)