I haven't read all of the posts, but I feel compelled to reply right now. I'm on my fourth t-shirt quilt,but this is the first one that I use stabilizer on the back of the shirts. When it came to sewing the sashing (actually I'm sewing a narrow border around each t-shirt before using the actual sashing). In garment construction I learned a long time ago to put the piece that is a little bigger (longer, most give, etc) closest to the feed dog. So I place the strip on the bottom and the t-shirt on top.(I pin at the beginning of the seam, about the middle, and at the end) As you are stitching the seam, just give a little tension (not really pulling to stretch) and keep on sewing (I use a regular quarter inch presser foot -- the one with the little metal guide on the bottom). Remember to place your pins perpendicular to the seam and remove the pin as you get to it. The feed dogs will gently ease the strip and your seam will be great. When you steam press, the extra fullness will be pressed flat.

edit: I've found that if the t-shirt has one of those 'rubberized" pictures on it, that will cause a little drag and the pieces will not feed well, so I kinda roll the block with the picture inside and hold the roll to guide the block through for the seam.