My reasoning is that everyone here probably has a goal of improving their own individual instrumental rationality, but that can't be a shared goal, since we have different preferences, and your improved instrumental rationality might end up being used to hurt me if we don't share the same values. Improving group instrumental rationality makes everyone better off, so that seems to be a reasonable shared goal.

That makes sense, I was aggregating 'goals that individuals here have in common' rather than 'goals that we can all cooperate on'.

About 'rationalists win' being considered cringe-worthy and/or inaccurate, is there some existing discussion about that that I'm not aware of? It seems like a perfectly good motto to me.

I don't recall a top level post on the subject, just many little tangents when it has been cited. People (I assume) all agree that it expresses a good point (along the lines of 'I don't care how well justified you make your decision, if it makes you two-box you fail'). The objections are:

1. Rationalist optimise winning rather than always winning. That you lose doesn't mean you were not optimally rational.
2. 'Win' is often taken to imply 'being first'. Rationalists don't necessarily maximise their chances of winning and unless the circumstances are dire usually take actions that will lead to them being near the head of the pack but seldom at the front. 'Winning' usually relies on poor calibration with respect to risk.

It is unfortunate that there isn't a powerful two-word motto that doesn't have any misleading technical implications. (I also don't imply that what you mean when you say 'rationalists win' is not entirely coherent, with these connotations accounted for.)