Well as far as the competition goes, I'd rather get pushed out than "win" by breaking from principles. That tends to get boring for certain partners that like the two bulls contending style of play. Ideally I'd push them out while maintaining the principles, which I'd count a true "win". Right now where I'm at in my practice I honestly get the most benefit from single hand circles, if I can find anybody willing to practice them. Let's see that competition instead of the handful of nominal single hand circles before switching to spaghetti arms.
So competing against myself, with improvement as the prize, not against some other guy with a judge and a trophy for the prestige of myself or my school. Too much motivation to win by any means at that point. That's how we get so far away from the real skill, IMO.
I'd never really considered the "bow stance" implicit in goat riding stance. I'd thought the angles of the feet were of critical importance there to meet that definition. Functionally, though, yeah I can see that if you're single weighted there, you can get some of the same behavior out of it. It reminds me of when I met up with Dmitri back in like 2008 and he stood on one leg and I couldn't do a thing to knock him over.
What I found worked for me, personally, in this goat riding situation is 1)single weightedness, 2) vertical pushing, not horizontal. If either of those was missing I'd just push myself back off. What I'm seeing in the little bit of the hour long video that I actually watched is that they're each trying to get under the other and whoever is lowest wins, when they double weight on top or bottom and try to push horizontally it just doesn't work.