I like your idea of the black sashing. In looking at your tee-shirts, this is what I would do: With the dark shirt in the upper left corner (Jets), I would take the other dark shirt (Hawthorne) in the lower right corner. I think the black sashing would be fine that way.
I have made several tee shirt quilts. Learned a lot along the way. First two were not stabilized and had to quilt by tying and hand quilting. Third one was double sashed and used too many shirts -- it was huge. But this one was stabilized with Pellon featherweight stabilizer (the one with the tiny glue dots on the back). It came out really nice, but as I said, we so heavy and large that I had to have it done on a longarm.
BTW, my first one was sashed with a novelty print and is very busy. The second one I used a solid khaki-colored cotton... ..much better.
Dina's idea for the black blocks like a winner.