My experience had no problem about booking at outside of registered country, too.
As you wrote, you have to book as a non-JMB member.
However, you can register your JMB number after booking complete by retriveing your booking record by booking reference.

Off topic:
For doometic flights, some advance purchase fare bookings don't appear in the account page due to JAL's limitation of IT.
(e.g. booking SuperSakitoku when still UltraSakitoku fare is available).