Let the iron cool. Take pieces of the shirts that you are NOT using (rags) and wet them. Then wipe down the iron. Next time you use starch, spray it, let it dry and then iron it. I made the same mistake with the last quilt I made.
I would love the see the quilts you make. I am making a floating stars quilt with my husband's old shirts (he tore 28 expensive dress shirts in the elbows even though we started buying him shirts with longer sleeves). My husband is 6'5" tall which means I have ALOT of material to work with.
BTW, unless you are entering your quilts into shows or selling them or doing a block exchange, the "scant" 1/4 inch is not that big a deal. I don't worry that much about it. Quilting should be relaxing and enjoyable!