If you're having difficulty with holding the fabric up, if you have a large enough flat surface, match up your selvage edges, lay the piece on the table and smooth the two layers from the fold to the selvage. Your edges will likely be mis-aligned at that point but you'll have the fabric straight. You could probably use a couple of pins on the fold edge to hold things in place if it's a large piece. I find doing the 'thread pull' technique very tedious with the cottons we use for quilting.
You could also try just working the loose threads from one cut end until you get all the way across the WOF. Line up those edges and that will give you straight of grain as well. At least that process you could sit for!