I finally determined that the 100W heater I had just couldn't keep up with the demand of printing at 80-100C, so I purchased a silicon 200W replacement and got it installed.
Removing the old heater's tape proved to be pretty time consuming, but eventually most of it came off:
But then it turned out that the new heater's temperature sensor was very close to the heating element, and didn't really tell me what the bed temperature was. Here is the surface temp while the heater is at 90C
So with that offset taken into consideration, I tried printing just the first few layers of a button base:
And it WORKED! The part printed very nicely, and we can finally, finally move on to printing the parts for user testing.
Coincidentally, the Hackaday Prize (and my own go/no-go evaluation) is about to wrap up and I'm nowhere near where I wanted to be by now. That's the frustrating part about setting abstract deadlines: meeting them can become more of a gamble than a challenge. Despite not having conducted the user testing that I want, at least I'm back in a position where it can happen, which is a lot further along than I was a month go!