MIG wrote:

Wherever I get on, if it's the weekend and I change at Kings Cross,
then presumably, even if I think my journey started at Stratford, the
journey that counts for the gripper starts at Kings Cross NR and
doesn't need an OEP, or does it?

I think it definitely does. The wording on the public Oyster site is:

"You only need to set an Oyster Extension Permit when you start a journey
within the zones covered by your Travelcard and want to travel outside those
zones on National Rail." It doesn't differentiate between NR and TfL
services at start of journey.

The internal briefing for TfL staff referred to earlier seems to be badly
written - but clearly they aren't operating NR stations. ISTM that briefing
NR and TfL staff differently is just symptomatic of the parochial nature of
these organisations...

Paul S