I KNOW you wanted specifically
DVC logo shirts, but I wanted to share this just in case........
To find the "bonus sizes" in the parks, go to the biggest shops....The Emporium at MK, Mouseworks at Epcot (found a great selection there), I can't think of the Animal Kingdom store (Island something I think). I also found several at World of Disney at DTD (but they went upstairs and got them for me).
ALWAYS ask because the bigger ones fall off the hangers so they seem to get stuck in the stockroom a lot so you kind of have to beg. (plus they can do that electronic inventory query that you mentioned)
One other FYI...........XXXXL seems to be smaller than 4X in the shirts I have--probably just a different vendor but tight in my rearend nonetheless

. I have also found 5Xs at the shops with more inventory but that is the highest I have seen.
I haven't decided if I am willing to go to the trouble but I might do this (for PERSONAL use only, not to sell--don't send the copyright police please): Purchase plain shirts and print out an iron-on transfer with our home resort logo on it and apply it to the t-shirts. You can buy that transfer stuff at Michael's, Wal-mart, or other craft stores......knowing me I will iron it on backwards, upside down, or something! Like I said, I haven't moved past "might do" yet.
grits