I've read reports of the supposed "formally administered Turing test" and walked away with the conclusion that the human judges were idiots.

The creepiest part of Voight-Kampff in Blade Runner was the idea that I'd fail it (not imagining myself as a replicant, but still as a human).

Do you have problems with your iris-contraction muscles and other involuntary muscle reactions? Because that's what Voight-Kampff actually tested. Supposedly, autistics and sociopaths would still pass it (as long as they were otherwise 'normal' humans).

I'd assumed that the VK test in the movie relied on knowing about the specific implanted memories that replicants had.

I'd assumed that Dick just pulled it out of his Bag of Narrative Props. Tolkein he was not.

Replicants could have been implanted with any memories. And if someone was manufacturing illegal replicants why would they be using specific memories that were known ?

It was about judging emotional response and relationship to subtle physical cues.

Any good descriptions of what it feels like to take part in a formal Turing test, and why it is so humbling?

The sibling comment (Bladerunner analogy/nightmare) is a great answer.