Frequently unresponsive 6s+ screen

For the last few months, my screen will often become unresponsive. This happens in apps, on the homescreen, and from the lock screen.

Things I've done to try to remedy the problem:

-hard reset

-using the 9.3 beta

-reset the phone and set up from backup

The next logical step is to reset the phone and set up as new, but I'd like to avoid that for obvious reasons. Any suggestions other than that?