I'm no carpenter but I'll try to offer valid suggestions. If you can't attach to the walls (Idid attach to walls in an apartment I rented, I just spackled and painted when I left) then you need to attach larger supports than the 1x2 you mentioned, at least in the corners. 2x3 firmly attached to your benchwork should do, you shouldn't be able to move it when you yank on it hard. The pressure the curved masonite will exert is quite a bit. Assuming you have 8' lengths of masonite, center them on the curves so the joints between them are as far from the corner as possible. Make sure your supports are vertical and use a screw at top and bottom. The bottom screw will be hidden, the top will have to be countersunk and spackled over. Concerning the amount of curvature, wetting (soaking) the masonite in water will allow more bend. Also, you can set a table saw blade to 1/16 and saw parallel kurfs (vertically) to allow more bend. Just be careful you don't snap the piece by trying to bend too much.
I'll relate what I did in one area, tho it was only logical to do it because I had a lot of free 3/4 plywood. I used that ply for the straight sections of my backdrop. I routed out the last 4 inches or so of the ply to a depth of 1/8" to match the masonite. I cut the masonite to the required length nad forced it into place, butting the edges against the plywood on either side. The pressure created by the bend in the masonite helped keep it in place, I just used some carpenters glue when the fit was right. A little sanding and spackling yielded a seamless backdrop.
Gary