The same can be said of any tax meant to curb a behavior (sin tax).

What traffic-reducing policy would you suggest such that all people are affected equally?

Depends how you define "equal". One approach is simply to scale the charge by income -- effectively, convert time to money, and charge you a congestion tax of some amount of money-earning time. "6 minutes" is 1/10000 of your annual income -- $2 for someone earning $20,000 per year, $20 for someone earning $200,000 per year.

But does a vehicle with several people in it pay for the max, min, median, average, or the driver's time? I suspect "driver" is easiest, it seems like it might work but I'll bet there are some screwy ways to game that rule, too.

absolutely none, which is why ideas like this will never see the light of day…

I think it's worth pointing out that congestion pricing is a policy that already exists in several cities around the world including New York City.

And also in essentially any relevant private market for goods and services where capacity is limited, especially when there are more and less desirable times.

In a very weak form, yes- and yet it still seems helpful and even popular after people saw the effects of implementation.