Okay, it seems that somehow the old (Java) version of the MC launcher interfered with the new one. I had to download a preview version of the new launcher from
here, run that and let it do its tricks, and only after that, the new launcher worked for me.
Glad you got it working. Definitely replace the old launcher with the new one. I'm not sure how the old launcher would interfere unless there were assets related to launching in ~/Library/Application Support/minecraft. So it
might make sense to make a fresh start by backing up saves, resource packs, etc., deleting the minecraft folder, then running the new launcher and putting those things back once the launcher re-downloads the game assets.
For what it's worth, you shouldn't have to download the launcher from that reddit thread, the download page on minecraft.net points to the latest version of the launcher.
One thing to note (which is pointed out in that reddit post) is that this new launcher requires Mountain Lion (10.8), which isn't explicitly documented on the minecraft.net download page - they only say, "If you are using an older version of Mac OS X..." with a download link to the (legacy) launcher.
Hopefully this this helpful to someone!