If they are announcing 90 minute delays, they will also add in a comment saying that you can leave and wait for the item to be delivered in a few days. So I would go to the desk, and see if they will record your details. If it's a simple booking and you still have your tags numbers clearly visible you can do this at home, the reality is that BA gets a huge pile of bags at the end of the day and they are not going to go through each item and assess whether you have been impatient or not, they'll hand them off to a specialist courier company and get rid of the problem that way.