I use a modified QAYG method for smaller, baby-type quilts and am going to try it on a bigger one at some point.
I prepare the whole backing and the whole batting (I use fusible Hobbs 80/20) Then I fuse the first whole strip of blocks to the batting-backing, and then continue sewing whole strips, fusing them, one at a time, either starting at the top of the quilt or in the middle, until the whole length is covered.
Once the strips are all sewn and stable, I can come back and FMQ the individual strips. The whole quilt is done pretty quickly! This can be done in a 'log cabin' center-out design too.