OK, I've been having the same issues on my 6 for over a week now with a replacement handset from the Apple Store. Spent 3 hours connected to Vodafonr tonight with them trying restores, restarts, recovery mode etc etc, in the end they recommended contacting Apple support. I did this and explained the following.
THe problem started with:
intermitant "No service"
SEarching in the signal bar
no carrier setting option in general settings
SIM card works in other devices
known good sims won't work in this device.
i Also noticed whilst on the phone to them that the device seemed to be looking fur a personal hotspot permanently.
AFter being on the phone to them fur over an hour they recommended they sent me a new handset out and I would be charged £29.99
i refused to pay for a replacement to replace a faulty handset they had given me 9 days earlier.
WHilst messing around tonight I have gone into:
Settings - Mobile data - Mobile data network - LTE set up (optional ) was blank, I've basically put exactly the same in them fields as shown in Mobile data, within seconds service has come back.
HOpe this helps some of you.
Mark