I moved this here hoping it would get seen better. Hope you don't mind. :)

I would think you could do it like a tee shirt quilt, with the stabilizer

I've been wanting to make a sweatshirt purse/totebag. A sweat shirt quilt would be very cozy.

I don't know about making a quilt out of sweaters, I bought a pillow made out of a sweater and I thought I can do that--I have lots of old sweaters.
I made one and that was it!! It was so hard to sew--just could not get my machine to sew it wound up sewing most of it by hand.

Here's the original post with some links.

http://www.quiltingboard.com/posts/list/4449.page

I think you could probably sew the sweaters by machine by placing typing paper on the top and under the layers. That way the knitting wouldn't get caught on the foot or the feed dogs. I've done that with terry cloth for that reason and it works well for me.

Pampered Chef parchment paper is the best non sewing thing to add to your sewing room, it is not as thick as other types of paper and I think if you put it on top of the sweater it will sew fine, try it & let us know.