Thought I'd report back:

I called up customer services (expecting very little!), told them the exact steps I'd taken to try to select seats online, told them that I'd called Iberia who referred me to BA (a white lie ) and within minutes the CS agent has seats reserved and they now appear in MMB.

After my recent, numerous, disappointing interactions with BA CS this was a great result and the CS agent couldn't have been more helpful.