I have two double weave projects under my belt, but have also been thinking of tackling a 2/2 twill. At this moment I have no idea how that works. I will take a look at that link Jane posted and my Jennifer Moore book. Anxious to see how yours progresses, Kathleen. Please share pictures! :)
P.S. Harrisville Shetland is great for blankets, but I know what you mean about color availability. It seems the colors I want are always out of stock. Good luck.
One more thing. Be careful of mixing fibers. On my first DW project I had added some Alice Staremore Hebridean 2ply in with my Harrisville. Bad choice. Though they look similar, they do not play nice together. I ended up have to cut out a big section of my warp. Lesson learned!