Blankets are often two layers. A front and a backing. Otherwise, that’s pretty much it. In a blanket, the layers are connected loosely if at all. ‘String quilting’ is an example of that (every foot or so a string tacking the material together.) So the person who had a bunch of T-shirts and a fleece back was likely the owner of a blanket. The easiest way to tell is to see if there are a bunch of patterned stitches running around seemingly randomly throughout the quilt. If so, they it’s a quilt. If not, prolly a blanket.
The stretchiness of T-shirts can be mitigated by glue on stabilizers. They are non-stretch fabrics infused with heat activated glue that you iron on to the back of the T-shirt.
That’s exactly what I would do. Tacking or tying is easy to do. Sew the t-shirt graphic panels together. Get fleece fabric to fit and use embroidery floss to tack it evenly at the cross seams. Bind the edges. Cool blankie!
Some of the younger people I work with have done that; it was some sort of fashion trend that just totally missed me. For the most part the result doesn’t look all that great unless you attach it to a much heavier shirt; a tee design onto a sweatshirt for example. Its like someone else pointed out about different weight materials in the sense of a quilt — when it doesn’t work it fails pretty badly.
My idea would be a photo-collage. Take a picture of yourself wearing each one. Then stitch the pictures together into a larger picture (I would go for a simple row/column layout). Have it quality printed poster size, and framed.