Another update. I don't know if it was something I did, or it would have worked even if I did nothing, but...
I can get the elements to light up if I hold the up/down lever all the way down for 2 seconds, and release it. Just shoving the lever down to where it stops doesn't light up the elements, but if you press it down a quarter inch farther and hold it for 2 seconds, the elements spring to life, and when you release it, the lever just returns to the place it was before, a quarter inch higher, and the elements remain glowing red until time to pop the toast up.
I had the toaster 90% apart when I discovered this option, lol.
I never had to forcibly remove the big tab I was worried about, so that's good.
I put it all back together, and it works again. I just have to spend 2 more seconds every time I use it. It still pops up at the right time, makes great toast, etc.
Thanks for all the replies. Chalk up another mustachian victory, eh?