When I add to the back of a quilt, I don't make blocks - I just use scrap pieces of fabric 4 to 7 inched tall and about 19" wide - or whatever I need to make it wide enough. Just a big 'stacked coin'. I set it 1/3 of the way in from the edge of the backing.
I can't do batting by machine - my zigzag machine distorts the batting so it won't lay flat. I butt the edges together and do a large whipstitch with double thread (by hand).