I drilled the hole in the case for connecting the Trinket. From the webs, I ascertained that I needed about a 1/16" bit (.0625 for a .067 screw). That worked. I was able to attach the Trinket, but I'm holding off on the final solution until I get through some of the following issues. I got some 2-56 3/8" screws, Philips head, and they work much better (I replaced the screws for the Piezo, also).
I put my meter on the circuit (DUH--learning the obvious lesson: do this DURING assembly to assure the connections will work).
First, I verified what the switch was telling me--I did not completely remove the trace between the pads on the backpack, so the circuit is always open and the switch had no effect. It looked OK to me, but I did some more scraping and now it works.
Second, I checked the LED connections. My meter showed continuity throughout. Using alligator clips to jump various connections, I could get one or the other LEDs to light, but not both. I desoldered one, and tried various combinations of connections with no luck. It occurred to me that maybe the battery did not have enough juice, but according to my meter it's putting out 3.96V, and it's rated at 3,7V. I also tried it connected via USB--no change.
Meanwhile, the Piezo wires came loose from the Trinket and I had to resolder.
I have posted a query on the Adafruit Support Forum about the LEDs. If I get an answer, I'll move on. If not, I may try it with 1 LED (which was the original design).