I would like to let the record note that this was being typed before The Red Jaguars posted their comment. These are the times that even Shaka Zulu can't beat.
Relax, it's just a game. I know it's a hard choice, but don't take it too seriously. This game would be boring if the choices were too obvious. If you don't like this game, then just don't play it, its simple. The thread stays open until the decision has been made. We are not starting a new topic, we are going to decide the winner in this thread. Sorry to sound rude, but I'm just being honest. You don't have to get so worked up just because the decisions are getting harder.
Like Joel, I can handle it

Sorry, I guess I was getting too wrapped up in it. I guess I was adding unncessary/unneeded/satirical wit to a tense moment.
But...since it has a full day...
My 2 cents?
#1 Lost Hornpipe, #2 Lucky Pillow.
This thread is to determine the best 'Temple Run' of all time, not 'Episode'.
What makes the Lucky Pillow episode so magical is watching a frail girl slowly progress into grabbing an artifact from the center room, not an easy task in itself. But, if someone had to sit down and watch 360 minutes of Temple Runs (yes, it shorter than 360 minutes, but still), her episode is just another solo win. Without the show background, the final effect is not as much.
Jessica and Jarrid were a powerhouse team. Neither spent too much time deciding or finishing a room task. I felt that Missy spent too much time in the Throne Room (remember the Guard pretty much shooing her away) and the Shrine. The only real mistake on Lost Hornpipe was Jarrid entering Secret Password for about 3 seconds, before he realized the Shrine/Bog door opened. Sure, that mistake could have been detrimental to the run if a Temple Guard was there, but at least Jarrid was sharp enough to get out, and not do anything really foolish like open up the cabinets.
Jarrid coming back up the ladder he went down? Brilliant. As anyone knows, that bottom level is a pain in the ass to finish, and time wasn't on his side. And unfortunately, he took the most direct route possible. Both players had to go up the shaft. A timekiller in itself.
IMO, the most astute thing in Lucky Pillow is Forest/Shrine. In Lost Hornpipe is Shrine/Bog/Shrine. The latter showed an epiphany that would be crucial getting out of the temple. Missy got lucky with there being only 1 guard in the most direct route to the artifact (Crypt could have had one, but we don't know). Jarrid/Jessica had at least 2 in the most direct (3rd and final if in the Cave. Since Tomb/Jester didn't open, and there was no guard in Secret Passowrd, the 3rd guard must have been in the Cave, unless LOTHT decided to stick the final guard in a room that was impossible to get to, unless Shrine/Dark Forest was open, but why would you go if Shrine/Bog was open?). The fact they had to have a teammate change shows how fast these people were. In comparison, Missy grabbed the pillow at 0:42. Jarrid grabbed the hornpipe after 2 guards and a substitution with 0:36. In terms of speed, she wasn't that fast, just kind of lucky, just like her pillow.
Jarrid and Jessica knew how the Temple ran, and they knew how to get back out. Missy had a great episode, but in terms of the 3 minutes at the end of the show, Joseph Wheeland's instrument is the one that gets to go to space camp.
But like LeVar Burton said "But don't take my word for it..."