We have now managed to book both partner flights we wanted given the technical error across 2 accounts. The process is agony, we went through multiple agents and the inconsistency in their training is astonishing.
I wish you all luck with your bookings. If you can, try and get them to hold the booking for you and email it to you real time before payment. We had one agent who heard 'December' as 'September', where this really helped.
You should ask to get the booking fee waived, but we gave up on this for our second flight after it took so long to find anyone competent enough to book it and it had previously repeatedly triggered hostility.
Do not ask for a supervisor, you will never get one. HUCA is the only option if the agent isn't competent.
This promotion, although generous, has convinced me I never want to fly Iberia. I have zero confidence in their call centres as a result of this and would never want to be caught relying on them in scenarios such as flight cancellations. We must have spent 2-3 hours on the phone to book 2 flights.