Tape is done...and usually even stuck to the wood...usually...
Overnight some sections of tape on the second panel's curves predictably came up. I got all of it back in place, and started using the copper-clad nails I bought yesterday to keep them down. When I taped the third panel with the tightest and most numerous curves I nailed some sections down as I applied the tape.
I've been adding nails wherever the tape comes up again. As things get sorted out I'll work on making sure the nail heads are as smooth as possible. The nails are 3/4", and the ends sticking out the bottom side of the MDF sheets make good places to tap in power.
Right now I've got the panels attached with C-clamps, and I'll have to spend some time considering ideas for bolting them together flush that allows adjustment.
Ran a few cars around, and showed the cats what happens when they cross the road without looking. They don't chase the cars anymore... First time I've really run the cars in over a year.