Getting a 11x13 camera could be a real challenge, as I have never seen a camera in that size and getting one built would be a long and tedious challenge, what you could do is use a standard 11x14 and mask the ground glass to the format you want to shoot and compose accourdingly when taking the picture, I doubt you would find much weight savings in having a 11x13 custom made over a 11x14 as the structural integrity of the cameras would have to be virtually identical.
Good luck, like I said, I have never seen a 11x13, if it was ever made, I would have probably made a screen for one by now.
Dave