I had the same problem with a queen size quilt! I use a lap hoop that is in a stand so I can use both hands to quilt. I love it. However the queen size had so much to move when I turned the quilt. I never quilted it in the summer!
So I bought a Grace2 hand quilting frame. It's great! It keeps the quilt off of your lap and the frame swivels so you don't have to deal with the bulk.
Here's a link to the site. It's expensive. I found mine here on the board for sale. I got it for $150. Perhaps you can find one used through Craigslist or...?
It came with the largest hoop which didn't work for my style of quilting. I bought the 14" one. If you did find one and wanted a large hoop, I would send you mine.
http://graceframe.com/site/hoops/hoop2