In James's position, I would say "Tell me who the straight guy is, or I walk." If walking is contractually forbidden, I would instead threaten to make the rest of the show unwatchable simply by not even feigning any further interest in the proceedings. You can make James stay, but you can't make him perform if he doesn't want to.
The movie-version scenario, though, is that James's mind works quickly, and after he says "Wow" he says, "I was sure I'd eliminated all the straight guys." Then he hints that someone on the crew was leaking information. When the producers want to know who, he offers to trade that information for the name of the last straight guy. He gets that name, then reveals that he's played the producers for suckers just as they played him.
Have I mentioned that I think the producers of this program are utterly despicable for contriving this setup? Worse than _any_ of the guys, straight or gay, who were toying with James; for the 'mates' were not, after all, the ones who thought this scheme up. For whatever it's worth, other 'reality' (hah!) shows with 'a twist' (what you do with a knife) like Joe Millionaire are just as bad.