A success! Updating here in case anyone else ever has the same issue.

BA told me they could add the three Iberia flights to my Executive Club account once Iberia confirmed they had been removed from Iberia Plus. Iberia said that flights can't be removed from Iberia Plus once added, but I would be able to transfer the avios. (A solution that wouldn't help me, as I needed the three valid flights to renew the Bronze membership...) This was after BA told me that it would certainly be possible for Iberia to remove these flights.
After a fair amount of back and forth and a decent amount of time on my part (where I often wondered if all this was really worth it), Iberia escalated my request and removed the flights from the Iberia Plus account, the proof of which I shared with BA. This happened on January 6th so I never did see the three flights updated in my account (the Tier points year refreshed to 0 on Jan 8th), but my Bronze membership remains, so something must have gone right!