Thanks for trying these. Can you try this with the 2nd version?
(Assuming Starfarer is in the Applications folder, if not, adjust path accordingly).
Open up Terminal and run these two commands:
cd /Applications/Starfarer.app/Contents/MacOS
./JavaApplicationStub
Normally, that would run the game - but since it'll fail, I'm interested in what the output of that is.
Also (and this may actually be more fruitful): take a look
here - you might not actually have Java installed, as apparently Mountain Lion uninstalls it as part of the upgrade. If this is the case, could you try installing Java (per instructions in that link) and running all three of the builds to see what they do?
Sorry to ask you to do all these things, and thank you for helping/being willing to try stuff. I really appreciate it.