I think a medallion quilt is the perfect candidate for QAYG. Piece the center, and add borders till it's a size that you feel comfortable with quilting on your machine. Then add borders using a QAYG technique. Remember, GAYG is a blanket term for many different techniques. I'd also suggest investing in Marti Michell's book "Machine Quilting in Sections:
http://www.amazon.com/Marti-Michell-...ng+in+sections
She has several different techniques that would work.