"Advanced Sanity" matches a strong comparative qualifier to a basic trait. While "sanity" has problems, as mentioned below, I think the phrase derives much of its power from its underlying pattern, which can be used in other suggestions.
Super Sapiens! ...I mean sapience.
Adroit Acumen
Elevated Erudition
Superb Sagacity
Crack Contemplation
The Singularity Institute wants to spin off a separate rationality-related organization. (If it's not obvious what this would do, it would e.g. develop things like the rationality katas as material for local meetups, high schools and colleges, bootcamps and seminars, have an annual conference and sessions in different cities and so on and so on.)
We can't think of a name for this organization.
We can't think of any names that seem good enough to be audience-tested.
We don't have any ideas good enough that we'd want to mention them in this post.
Help.