I was taught to do as you do - baste the top first, then the sides as they are exposed when you advance the quilt to the next area. I use a centering tape measure to make sure the block seams stay lined up. Quilt top to bottom (but then, I don't do medallion quilting - that you'd probably start in the center). Baste bottom when that's exposed, again still using the centering tape to make sure the blocks stay lined up.
I think if you're getting a lot of fullness (and increasing fullness) as you get towards the bottom, then the sides of the quilt are drifting in as you go. Once that starts and you don't address it early (checking/adjusting block alignment), it compounds as you go.