iCloud not syncing to iPhone

I have a very odd situation here that the Apple Support team hasn't been able to figure out. I'm hoping someone from the community has an idea that can help me.

Contacts, Calendar & Reminders stopped syncing to iCloud from my iPhone 6 a couple weeks before the 6s launch (note: iMessage & Photos were still talking to iCloud). I figured there was something buggy with the 6 and that the problem would 'solve itself' when I got the 6s. It did not. Initially, I restored the 6s from a backup of 6. I've tried restoring the 6s as a new phone and attempting to sync to iCloud, but this didn't work either. I've tried creating a new iCloud account and trying to sync that, but it didn't work either. It's important to point out that iCloud is still syncing to my MacBook Air and iPad, both ways.

It wouldn't make sense to me for the problem to be just with the iPhone since the problem has existed on 2 different iPhones.

It wouldn't make sense to me for the problem to be just with the backups since I've tried restoring the phone as new.

It wouldn't make sense to me for the problem to be just with the iCloud account since I've tried syncing a different account.

It also wouldn't make sense to me for the problem to be user error because I'm pretty experienced with iCloud & iOS and I've also had Apple employees on the phone and in the store walk through the set up and sync process with me to confirm everything was done properly.

What's weirder about all of this, is that after all of this turning on and off of iCloud none of my Apple iCloud-related apps will work now. I can't add calendar events, I can't add reminders and I can't add contacts from my phone.

I'm out of ideas on what the issue could be or how to solve it. Short of making a sacrifice to the iCloud gods, do any of you have any ideas??