Having the same problem. Started getting random screen input several weeks ago on a Surface 4 purchased in 2016. Support suggested disabling touch screen drivers to stop the random screen activity, then reset the machine to factory state. They thought it was a software issue. Then I noticed the screen bulging on the left side. Now I'm back to using a 12 year old Toshiba laptop which runs okay (on AC at least).
I too would have been happy with a good deal on a Surface Pro 7. Kind of PO-ed that they washed their hands of this problem. I always figured the battery would degrade over time and not hold a charge. I did not expect my Surface to become a FIRE HAZARD.
I never thought about UbreakIfix. There's one in my neighborhood. I'll check them out.