I know OP has already done one quilt at home and will do the next one at the laundry mat. But I thought I would share how I wash rag quilts at home.
I have a top loading washer and have made 5 small and 3 twin sized rag quilts. I wash at home, but my machine has a presoak cycle that does not drain. I use the heavy duty cycle and once it has agitated I use a colander and strain the water until I am only getting a few small bit of thread. Then I reset the machine to the beginning of the soak cycle and repeat several times. When it gets to the point I am not getting as much thread, I let the machine complete the wash cycle.
Then it is into the dryer. I find that by doing the long agitation, and straining the threads out of the washer, I do not get as much in the dryer lint filter.
I have used two layers of flannel, a layer of flannel and a layer of denim and two layers of flannel with a layer of thin batting.
I would not attempt a quilt larger than twin sized in my home machine.