The way I do it is that I first lay out the batting with just one of the floppies on top. I usually use spray glue to baste it down. (Is calling it a floppy better than calling it a flimsy? lol) Then, I use a long doll needle and dark thread and do a really long running stitch about every 12" or so, horizontally and vertically, and around the edge to create a grid to use as a guide on the reverse side.
Once I have the grid stitched down, I flip it over and use the stitches as a guide to lay out the reverse quilt top. I'm able to line everything up all the way around pretty accurately.
As for the actual quilting, I am barely learning to FMQ, and the only stitch I can do somewhat adequately is all all-over loopy meander. So far, I haven't had any trouble with bulky seams, although I have to admit I skirt around the intersections of blocks where that might be a problem.