I tend to agree with what your did. Fire on final- land ASAP. I suppose you could have the PNF make a quick radio call "Fire on board, unable to GA. Landing runway 23". That way, ATC wouldn't put you in a situation where you needed to GA.
A similar thought occurred to me last time I went to Atlanta. We were ~3nm on final when they had a 757 cross the runway. What would have happened if the 757 got stuck on the runway and I was unable to GA?