I do start out with larger background pieces, too. They do tend to shrink a little, and then I square them up when I am done with all of the applique work. You will find that after starching, there will not be near as much distortion to the block :wink:
If you decide to use a tear away stabilizer, you may want to tighten up your stitches, and shorten your stitch lengths, so when tearing it away, it won't distort your stitches.