I did my last bed quilt in three sections, since I can't get a full quilt through my machine either. I had the batting and backing in three sections also, then joined the fronts with a sashing strip and overlapped the backing and hand sewed it.
But your method sounds very doable. There is now iron on tape for joining batting pieces together -- if that would make you feel more confident.
You could search quilt as you go on this Board, and you'll get lots of topics to look at.