I just thought of something that I don't think anyone's mentioned yet. After you wash your sweater, you should be able to safely use the spin cycle on your washing machine for about 10 seconds to get the excess water out -- I'm talking about the cycle where it just spins to pull out the water from the clothes after rinsing so no water or agitation is involved. (You should probably put it in a sweater bag first.) This should reduce the amount of towel blotting you need to do before laying it out.
As an aside, I have successfully used an ionic hair dryer to hasten the drying process of superwash wool. You probably wouldn't want to try it with non-superwash wool, but I thought I'd mention it. I had a hank of sock yarn that I wanted to dry, and the blow dryer was much more effective than tucking it in a pillow case and tossing it in the regular dryer.