I recalled that SPX (and for that matter, SPY) options do trade 'after market', when presumably liquidity is lower, so one might think that could lead to wider bid/ask spreads.
I called the Schwab options desk and asked them if their data posted on their website when normal markets are closed e.g. after 4:00pm or on weekends or on holidays etc, was "close data" or if their data reflected "after market" activity?

They replied it is "close data" and does not reflect 'after market' activity.
So that ain't it for the data I was using (maybe RayVT uses a brokerage that posts after market data?)

I also gave the options desk guy one of the examples I posted here, and he checked it in real time.
"Negative extrinsic value!" he said.
Yep, that's another way to say it.
He contacted their "trade resolution desk" and apparently the reply was that "yes, you can have negative extrinsic value for SPX options". He said that he'd research it more and send me a message. The "official explanation" will be interesting.

The explanation that I came up seems correct but slightly unsettling: SPX, unlike SPY, has no shares and hence there's no arbitrage mechanism for SPX that keeps extrinsic value positive. I believe that to be a true statement, but feel like I'm missing something e.g. an expert might reply "that's true, but you neglected this".

An alternative explanation is that it's market makers just messing with our heads.