If you are sharp with the DiY, I don't see a major issue with doing this. It is quite likely the screen will have some significant waves to the material as rear projection surfaces tend to be somewhat thinner than front projection surfaces.
Companies like DaLite offer Dual Vision and similar surfaces which are available in motorized tensioned screens. Think... $3,000ish for a 133" diagonal.
I would probably get some material from Carl's screens...https://www.carlofet.com/shop/projector-screen-material?screen_material=White+Rear+Projection&finished_edge=Raw+Material&seam=Seamless
They offer it in white and grey. Might be worthwhile to try out both to see which you prefer. I would likely use the grey material with a bright projector and call it done.
Not sure how you end up doing everything.
I did one in my one-car garage setup. I just screwed a couple of 2x4's into the garage frame with the door UP, and I had a flat bed sheet stretched between the 2x4's. It wasn't great, but it was 'fine' for the kids outside to watch. So, don't count on serious quality here. Also, you will need to deal with audio separately. Projector audio sucks.
- Theater, whole house audio, and technology consultation during the build and installation process in the Washington, DC metropolitan area.