Touch response dead zone on iPad Pro 12.9.

I have a 12.9" iPad Pro that's a little over two years old. As a musician, I use it constantly with forScore to display my sheet music, and it's been fantastic! But I've been noticing some annoying missed page turns in the forScore, and other missed "taps" in other apps in the same area of the screen. So I decided to do a scribble test in a drawing app, and lo and behold there appears to be a "dead zone" to touch response that is a strip about 1/4" wide spanning the screen, starting 3/4" away from the home button. See the attached image. I didn't purchase the extended AppleCare protection plan, as I take excellent care of all my iOS devices, have never dropped this iPad, and have never had problems with any of my iOS devices in the past. I may reconsider that decision with my next purchase. Has anyone ever experienced this, and found a solution? I expect it will be a hardware issue, and probably an expensive repair, so I thought I'd reach out to this community first, just in case any of you have suggestions that might save some money.

As an aside, the home button has also been "sticking" so that it audibly clicks when pressed, and I need to press it firmly to activate it. It's almost as though something sticky were spilled on it, though I've never spilled anything on the iPad. It still works, including the touch ID, despite this "sticking" issue. I wonder if it could be related to the touch response problem?