"Your troubleshooting has been very good and you have eliminated quite a few things.
Has your phone been dropped, repaired or even opened out of curiosity just shortly before you had problems? Did it come in contact with water or high humidity?
My thinking is that one of the internal antenna connections may have come loose. The fact that your phone sees the IMEI generally rules out a baseband IC issue. If you're comfortable, you could open up your device and look for anything out of place such as disconnected connectors, red water indicators etc. However, tread carefully, disconnect the battery first (especially on the 6S) and don't force anything."
"Try this: Hold down the power and home buttons to turn of the phone, and keep them depressed until the phone restarts itself. Continue holding these buttons down until the phone then turns itself back off. Wait a few seconds, then depress them again until it starts up, then let go of the buttons. I've heard this has worked for some people.
I have also read about the ""drop technique"" where people put the phone in a case then drop it from about 6 or more inches onto a hard surface with the screen facing towards the ceiling. I wouldn't personally do this until I've tried everything else but many people have backed this technique."
