After a week away and devices idle, I returned to find that Z802 and Z441 had offers of ESU enrollment, which I accepted, making 9 enrolled. I found my way around the endless loop on Z601 by switching from a local account to a windows personal account and bypassing the bizarre refusal to recognise my password by logging directly into the personal account with a one-time code, and then confirming it with the password (which for some reason was now acceptable), after which (and a restart) it behaved as others had done. So that's 10 enrolled. Z603 seemed to have the same problem as Z601 but didn't allow the same solution. Z805, my NAS backup device, a battered Z800 with 6x 4TB drives in RAID10, also received an offer after I updated it and restarted. So in summary the fact that it is a dual boot W10/W7 device wasn't a problem. So I'm nearly there.
So far my conclusion is just that (1) the W10 device should be updated, and (2) the W10 device has to have been registered
at some time with a
personal Windows account (connected with email/phone no). The ones that were running with local accounts but had been registered with the personal windows account in the past seemed to get the updates without a new registration, but some didn't, and after I changed to login with the personal Windows account I got the ESU enrolment but (as yet) haven't found a way to revert to a local account login.
Edit 23 Sep: Updated UB1 (2013 Toshiba Satellite Z930) and on restart it was offered ESU enrolment.
@ toTOW: Somewhere in all that I recall a statement from MS that the ESU offers would be on a different timetable in different regions.
@ BobWilliams757: If the device has
never been connected with a personal MS account it might not get an offer.
Edit 27 Sep: 2012 vintage Sony Vaio SB36FG laptop received an offer after updating, followed by strange result when accepted: message that I needed to be connected to net, which I obviously was since how else could I get the message? Figured it was a hint that accounts were local and it wanted a MS one. Added MS account (admin) and enrollment *(Settings, update page) was offered, accepted, completed. The same process then worked for Z603, after working around non-recognition of valid MS A/c password with email single use code. All W10 boxes now enrolled for (free) ESU

Edit 4 Oct: 2013 vintage HP15 Pavilion (p010AX) with AMD A10 5754M enrolled after adding user with personal MS account.