Finally, my problem is resolved; unfortunately the solution is a little less than clear.
Since I was able to replicate my problem while I was at the dealer, I left my bike with them again to see what they could do. They said that they found a fault code in the ECU when the bike was running very, VERY hot. The tricky part was that these fault codes are supposed to be stored by the system so they can be read latter, but this one was clearing itself. Once they found it, they decided to replace the ECU.
The thing that made me skeptical about this solution is that the problem they found is not the same as the problem I've been having. My bike would run poorly when it first started up in the afternoon after sitting all morning. Thankfully it runs great now, as I was riding around in 101o heat yesterday with no stumbles at all.
What this means is that either they found a different symptom of the same problem (the ECU), or something they did after replacing the ECU fixed the problem (reset TPS, removing and reattaching connectors, etc.). It's possible that, if my ECU was having problems with high ambient temperatures, by getting the bike extremely hot they were able to create a local ambient temperature that caused the same problem. Just a theory.
In any case, I can finally start putting on miles again.*
If anyone else has problems like these I hope their closest dealer/shop is closer to thier climate than mine is!