Pam, I cut squares of calico and batting a little bigger than the finished block then sew the log cabin directly on; I don't even pre-cut the strips - just trim them square when sewn on. Then you just trim the blocks up and piece then QAYG method - pieced and quilted in one hit! You can always add a second, decorative backing if you bon't like all the seams on the back and just ditch quilt round the blocks or tie to hold it. I've done this with my own cut strips but keep looking at jelly rolls thinkin - got to get some of those, bet I could make a quilt in an afternoon!
K x