realistically we're looking for much higher (sub 1%) cognitive ability. I understand this is highly sought after, so we incentivize by paying a few times what FAANG does locally.

I was genuinely wondering how OP preferred to be approached vis-a-vis this sort of assessment, since they suggested that they would walk out on conventional approaches. I mentioned cognitive ability and ability to learn as I feel those are harder to extrapolate from one's existing publications/contributions/take-home assessments, compared to in-person discussion(s).