Although the title of this thread is QAYG your question seems to be more about the different quilting designs you can use if you don't want to do FMQ. The purpose of QAYG is to do the quilting in manageable sections and then join them together.
Ininei is the queen of both techniques and I'm sure she'll chime in with lots of advice, but one thing I'm sure she will say is to use a walking foot to greatly reduce the chances of the layers moving around as you stitch.
There are different ways of doing QAYG. The link Snowgoose posted tells you to trim the whole block so that when you join you get double thicknesses of wadding which was claimed not to affect the appearance, but I'm doubtfult of that.
Another way of QAYG is to quilt the blocks and then trim them, then butt two blocks together and cover the joins with sashing strips.
Alternatively you can quilt one block (or strip of blocks) making sure that the quilting doesn't go right to the edge. Then join another block (or strip) of pieced top to the first one and another piece of backing to the first piece, flip them over and slide in another piece of wadding (batting if you use American terms) and then quilt that section. That's the way I made the wedding present quilt earlier this year. Full discussion about it
http://thesewingplace.org.uk/index.php/topic,1589.0.html