Originally Posted by lab fairy
Are you pressing with steam? If you are, try turning it off. Your wrinkle problem may be an issue of too much heat.
When I've worked with t-shirts in the past (I haven't done this type quilt though) I used a paper bag or piece of cardboard inside the shirt to give it some "stabilizing". My SIL has made many of these type things and her solution was to cut out the "important part of the shirt and applique onto a foundation.
It sounds like you're doing really well. Your fabric choice looks good. Have faith in yourself.