Thanks for your interest and perseverance, Mike.
It seems like the key might be in this mysterious routing on the smartcard, R40232. That only appears on the Amersham record on the card; the expired records for a z1-6 have that field empty but are otherwise identical apart from the dates. So if the gate is reading only the destination R1256 then one can see why it would reject. I’ve only just realised that at no time did I look at the gate reject code: the red light on the reader was all I was focussed on.
I look forward to learning what you discover, and I’ll post TfL’s reply.