Having just finished one t-shirt quilt and almost finishing another, I will say you are a brave person to want to hand quilt one! I will admit half of my shirts were sweatshirts, not t-shirts, and they were a real bear to machine quilt with a domestic machine! I agree with Rita about maybe trying Mistyfuse. It is supposed to stay quite soft. (My Pellon 911 sure didn't!) And, the light weight iron on tricot that Kathy and Eileen suggested sounds like something I may be trying in the future!
Might I suggest that you take some of the backs of your shirts and make some sandwiches with the batting and backing that you will be using, and try some of stabilizers that have been suggested, and see how well they needle. And, then visualize doing 9, 16, or 20 of them!
Good luck!
Dawn
In beautiful Northwest Montana