I've seen a QAYG method where the blocks of the left hand column are joined, then layered onto columns of batting and backing and then quilted upto 1.5" of each edge. The next column of blocks (second from the left) is joined to to the first column before that column of batting and backing is added. This column can then be quilted including the part of the previous column that hadn't been done. The next column is added and so on until all columns have been added and quilted.
Whilst you will be wrangling a larger and larger amount of quilt, no more than the width of one column will be under the throat of the machine. I confess that this is still on my list of things to try, but if you want a go you will find a tute on Youtube.