Good advice....tnjacke.
Or work on an easier quilt as your main project or finish some UFO's and use the thousand piece one as a diversion when you need a break from sewing. That way you can at least see the progress on one while you are cutting the other. ...you'll have it cut out and ready for sewing before you know it.
Another thing that might help is to vary the colors when cutting...don't cut all the pieces of one color first before going on to the next color. Make a copy of your pattern and check mark off the steps you have done.....go back later and do the subcuts if there are any. That always helps me.