Log cabin patterns always go so fast for me. If you do simple patterns and split the colors on a diagonal, you can arrange the same blocks a bunch of different ways to make "different" quilts. You might want to cut all the fabric before your knee surgery, but after that the chain-stitching is fast, and all you'd have to do is stitch, cut, press, repeat for as many blocks as you have fabric for. I have a spreadsheet worked up that tells me how much of each fabric I need for a certain-sized quilt, and if you like I could work up the numbers for you for whatever dimensions you were planning.
Also, to keep it simple, I'd suggest making the backing a flannel, then just folding it over the sides to the front for the binding. Quick and easy, and soft and warm
