I think it's safe to say that the average TPIR fan wouldn't really care one way or another if Rich Fields gets any face time or any extra interaction on camera, but I thought of two ways to give Rich more face time.
Come to the show with a LARGE pic. of Rich Fields on your shirt. Ok, maybe you won't get called down, but you may be able to get on camera.
(I thought also of maybe a large blown up photo, but I am pretty sure the TPIR staff wouldn't allow that, since it might be considered a "sign", and they DON'T want to be LMAD. I remember on one trip to TPIR, a group of people wore halos with mistletoe on them. They were asked to remove the halos... I guess it fell into the category of a "costume")
If a contestant wins his/her pricing game, make a run for Rich Fields and shake his hand or whatever. You might scare the heck out of Rich, but the cameras may at least capture him on camera.
Note that I am not suggesting these things as SERIOUS suggestions, but I am surprised that nobody ever thought of doing this when they were on the show.