I was always off-put by QAG because of the need for sashings and often hand sewing of sashings. However, this is a method I would be willing to try:
https://www.candiedfabrics.com/2013/...ing-as-you-go/
Here is a slightly different QAG method, but it does not completely eliminate the "wad under the sewing machine arm" problem because the backing is added last:
http://www.accuquilt.com/shop/go-big...arter-set.html