I have the Midnight Special episode in part but Dennis sings Angel Come Home not Good Timin'. Unless others can confirm it aired, I think it may have been from a rehearsal for it.
I finally got a more developed explanation of this from a reliable source...yes the rehearsal was taped and i think the circulating Good Timin'/Midnight Special audio is from that. However, Dennis' Good Timin' performance was apparently also filmed for the broadcast along with the other songs we've all seen that were on the show...but it did not air because he messed up the words. The footage is in the Brother archive from what I understand.
I'm pretty sure that I read somewhere that some time after the Midnight Special was taped, Dennis overdubbed his vocal on Angel Come Home, because he was "impaired" and made a mess of the words. Can you confirm this? I suspect that whomever said it(I can't remember the exact source) might have just got the two Dennis led songs mixed up. Dennis does seem to cover his mouth/lips with the microphone for a good portion of Angel Come Home, though.