From what I understand, I believe the tire is a ECSTA Supra variant. The rear tire from specs will likely be about 3/4 of an inch shorter in rolling height.
From other limited conversations that I have had post sema. Yokohama also has something in the works that may work and I have heard that Dunlop does also. Nothing official and nothing in their catalogs, just by asking have managed to see what they might have coming to help us out. Kuhmo is kind of the same way but it seems that they might be closer to coming into a "sales" ready application. The best place to start if you want to approach another company other than these is to ask for the head of motorsports development or similar. Those guys know much, much more than the sales guys that only know what is in the catalog.
Sorry to take so long, but I have a couple of personal happenings going on right now and my attention is more focused on those rather than the GT.
Thanks for being patient.