There is some precedence from ISU with this where they went the general admission/standing room only route in a somewhat similar matter (they were labeled standing room only tickets). The game in particular that comes to mind was two seasons ago in the last game of the Big 12 season against Baylor. Since the students were a bit hit or miss at the time in completely filling up their full alloted seats, ISU sold a bunch of GA/SRO tickets that game to make sure the place was completely packed. I actually bought one of those GA tickets. The end result was what JP was looking for as I've never seen so many people in Hilton, but I do remember a few that were stuck standing to watch the game as well, but not many. I also do remember a few season ticktholders griping about having to kick someone out of their seats, but not as many as I expected.
Sorry to bring up ISU here, but I just do so to say that something similar has been done for a sold-out game before. I'm also not necessarily saying it should or shouldn't be done either, Just using it as an example.