Drop cloths will certainly hold up better than muslin for slipcovers but might be a bit of a pain to maneuver. Duck cloth is also an option - very comparable to drop cloths but don't know for price comparison...might want to check some of the reliable fabric sources for that.
As to roman shades...I used quilting cotton/batting and did not have much of an issue. I think I made 3-4 for a total of 2 rooms. Cost wasn't horrible. Piece together batting scraps. I did 'inside' window measurements. If you're looking for light control might want to go a couple of inches beyond 'outside' window measurements. And you'll need the tape w/rings to place on the backing fabric. Also tricky to hang unless you do a small pocket to use a tension rod but then pulling the shades can mess up that arrangement. Just some thoughts.