I'm on my second passport, and at least second ESTA, since getting GE.

The ESTA is largely irrelevant - that ties to your passport, and is needed whatever entry route you use. It's not a component of GOES, although no doubt the various immigration portals talk between themselves.

I've only ever updated my passport (and driving licence, although I suspect that was a pointless exercise) in GOES. I've never had the X, nor had a GE machine refuse me in any way. There's probably something else, quite possibly bad luck, that's causing the OP to be sent to secondary.