So, I took my unresponsive iPad to the Genius Bar in the local Apple Store. Not a perfect experience, cuz they couldn’t fix it, but here’s two things:
A) they didn’t charge me for spending 15-20 minutes trying to fix it for me, and
B) the tech and I both agreed that getting a new screen kit from iFixIt and fixing it myself was the way to go. I didn’t even know that was an option. It’s fifty bucks. A lot better than $300+ for a new iPad. 👍