Thanks to @TomSuperO, the backdrop is up!!
His patience was key in sticking-unsticking-sticking-unsticking-sticking-unsticking-and finally sticking a portion of the backdrop through a dip in the masonite. The masonite curved toward the wall at one section but the curve was not vertical or perpendicular with the floor. Consequently, the backdrop would not go on smoothly without a ton of work, which @TomSuperO did. I wouldn't have had the patience for it. I would have yanked that masonite down and got sturdier plywood so I had a flat surface to work with. For what it's worth, the dip occurred because the concrete supports stick out farther than the 2x4s. I tried to ignore that. Lesson learned.
Here's the method we used:
1.) Put that fancy double sided carpet tape in two stripes where the top and bottom edges of the backdrop will be. Make sure the stripes are level. Mine were not level and it's a pain to deal with.
2.) I discovered Scotch Delicate Surface Tape on a whim at the grocery store, of all places. We used a lot of that tape to temporarily hold the backdrop up. You can't just yank it off the paper backdrop but if you slowly pull it away, it will release without damaging the paper. Pretty impressive and very handy. Using it at the top and bottom makes the next step tricky BUT it does make adjustments MUCH easier and I think it's worth going this route because of that. We adjusted the backdrop three times before using the double sided tape to permanently stick the backdrop up.
3.) Working in roughly three foot sections, we took the purple tape off and started pulling the backing off the doublesided tape underneath as shown:
The trick was keeping the backdrop close to the tape, without sticking it to the tape, while you kept the backdrop taut and free of buckled sections/waves/folds/etc, and then pressed it down. It's tough but we got it 99% right. The dip/bend in the masonite was the killer and it's as good as it can be.
You repeat that last step with the bottom, pulling the backdrop downward.
I'm extremely pleased with the results. I did cut it at the right angle in the second picture but it was necessary to make the job faster and easier. This will be hidden for the most part with a mountain anyway so I'm not concerned. That makes for one section a bit over 40' long, and another around 10' long. There will be some necessary cleanup along the edges of the backdrop like removing visible tape and painting the surface black.
The next step will be putting a ledger board up along this wall to support that side of the table. Then it's table time!
Here's to hoping I got a table with a loop of track in the month of June!