Keep in touch with your pleasant highly functional sane ex-coworkers and use your network to vet companies/orgs/teams.

Personal referrals are the way to go. I don't think you can really assess a company for pleasant/sane working environment unless you know someone who works there (who you can actually trust to tell you if it's a shitshow).

Try to start one on your own?

Most likely this will be anything but pleasant, but if you are very careful about not accepting VC financing you may try to optimize for sanity... highly functional will come mostly as you learn from your own errors.

I've been thinking about this for a while. I think it would involve asking a highly focused set of questions to at least 3 different employees and see how much they correlate. I don't know what those questions are though :)

One question that I think correlates low with a highly functional sane tech company is "Does your CEO still write code for the product?" if the answer is yes and the company is larger than 20 people, odds are high that the company/CEO is not highly functional.

Ask all your interviewers: "Would you recommend <company> to your friends?"

You know what to do when each of the 3 interviewers of your on-site give a blank stare to this question :D

I have found the smaller subproblem of just finding a pleasant, highly functional, sane company to be almost intractable on its own.