And now for the rest of the story. If anyone sees this condition it is dangerous. There was a fairly tall yellow flame coming up from around the gas jet and up past the metal shields, extending up maybe 6-8 inches which I assume is what caused the melted wire connectors.
---I shut down the LP immediately, and threw some ice bags in the fridge to keep the food cold until we got to our destination and could check things out in more detail.
Took all the shields off, cleaned soot and any other stuff up, and cleaned the gas jet as best as I could with a bread tie wire, and everything seemed to work fine after that. It very well could have been some bugs/gnats that got up in there and it was enough to throw the whole system out of whack (and create a somewhat dangerous condition).
I went ahead and did the same clean up treatment on the gas water heater system as well, it was working, but did have some soot and "funk" going on as well. Better safe than sorry.