JAL's seat selection (at least on international flights) has always been an unnecessarily complex procedure. I can echo your pain having booked last year on a BA-codeshare.

What I understand is that seat selection is free for the elite plus a companion. The elite can assign a seat for themself, and the companion's seat has to be reserved over the phone.

I was able to do the seat selection in the end, by using another airline's website. I used Royal Air Maroc to pull up the booking and used their seat selection for myself (or in your case, the BA Gold/OWE member). You could also try out the Royal Jordanian or Finnair website.

After my seat was confirmed, I had to ring up the JAL call centre to allocate a companion seat (elites are only permitted seat selection for one travelling companion). I called the European Call Centre, who I had to stay on the phone for about an hour before they could allocate the companion seat. However, this appears to be more of a fluke than a regular occurance as their official rules indicate that the tickets had to be issued by JAL to avail seat selection this way.

I hope it works out for you - good luck!