I don't know how well it would hold up, but you could add a layer of heavy vinyl (clear or other) to the back of a quilt after it's quilted by sewing it on in the binding. I don't know what the cost would be. It comes in different weights. You might need to use a roller foot to get it through your machine.
The plarn project is a wonderful way of encouraging people to help by investing their time and not money. I don't know of a way to do that with quilting. Many quilt guilds do charity work and there are plenty of people in shelters who would benefit from a conventional type of quilt, and of course, there's also Project Linus.