How important is this shirt to the quilt?
If it is a client quilt, I think you would be best to discuss your concerns with them ... and make it very clear that you cannot give them any certainty about how it will stand up. Perhaps the peeling effect is fine with them because of its significance. And too, they may say, just leave it out.
Obviously, they have been around similar T-shirts for their normal use, and know whether that is a bother to them ... and perhaps they like that worn out effect!
As for the steam-a-seam, I'd be hesitant that it would provide any long term satisfactory results.
Thinking way out here .... Wonder .... is there something you could put over the whole thing? like a clear film?