Actually that (a frame) is your idea.

I sort of tape the bottom shower curtain to the bottom board. Roll the curtain a wrap or two around the board, then screw into place. Repeat at the top. Then add additional boards to secure and prevent flapping. But your idea of a premade frame is much better. It would also allow a better fit. You can see where the curtain has some wrinkles. I am not much of a builder. Using the Home Depot 4 mil opaque plastic might be just what you need. And could be removed each spring. I guess next year I have a new model.
Here is a picture with one side partially installed. Your frame idea is either genius, or I need some remedial building lessons.