Diving into sewing projects
So, I grabbed an empty wrapping paper tube and used it to roll up the fabric! I will admit that a number of my space issues are very self-inflicted (as you may have picked up from the picture above), but even if I had cleaned off the whole table before starting, I still would have rolled it.
Rolling up the fabric lets me have it rest off of the table while I'm working. This frees up more room - no big bunch of fabric at one end. Also, the cat stays off it, and it helps cut down on wrinkles.