OK - in case anyone finds this thread with a similar problem in the future (I couldn't find many that didn't talk about the same 3-4 possible issues), here is the conclusion...
Long-story short, it was the 30a breaker at the camp's power feed.
Where I got thrown off was in the fact that the AC unit would not immediately reset and operate. When the 30a tripped the second time, my first move was to switch to the 50a feed (which, it turns out, was the eventual solution). However, this immediately started to call for the AC to work, and it never did. As I switched between 50a and 30a, trying different things, nothing worked. The key here is that I was ALWAYS calling for the AC (never allowing the system to reset). It wasn't until I let the fan run on its own for a while, with no call for AC, that the system would reset and properly operate again.
Once I did this, late yesterday afternoon, it ran for a while before tripping the 30a again. It was at this point that I rested the system again, switched to 50a, and it has been working flawlessly since then (around 8:30p last night).
So - the moral of the story is, at least in my case, there needs to be a 'waiting period' after a blown circuit, during which time there is no call for AC from the thermostat, before the AC system will reset and operate correctly.
I don't know how long that waiting period needs to be (all I know is it is more than 5 minutes and less than 45), and I don't know what it is that is taking that time to reset (thermostat, compressor, etc...). However, I do know that had I simply switched to 50a (which I did do) and let the system rest for a while before rebooting it (which I didn't do), it would have avoided all of my issues and saved me about 4-5 hours of frustration.