I would strongly suggest stretching muslin across 1x4s that have been attached to the floor, stapling the muslin to the "frame", sizing the muslin with starch, and then painting it with good scenic paint - 100% acrylic, rather than casein-based house paint. The muslin will tighten due to shrinkage, but once it is dry, you can remove it from the frame and it will be fine. Using the acrylic scene paint, the muslin won't behave much differently than if it was not painted. That is how backdrops are done in the real world. You might need to seam the edges to hide the spots where the staples were, but it works quite well. Muslin certainly comes in widths sufficient for your needs.

You didn't say anything about what you planned to paint on the fabric. I am assuming it will be a random pattern, rather than a detailed image. Keep the paint pretty wet - if you use Rosco Super-saturated paint, you can dilute it way down (more than 10:1) and get watercolor-like effects. Great stuff. The stuff isn't expensive, but it goes really far, and works much better.