Just wanted to report back on this. I did a little more detective work by calling the main airport number. After a couple of false starts by being put though to the main BA reservations call centre, and then the local airport Lost and Found, I was eventually put through to Swissport who handle lost baggage, who told me I needed to contact BA locally, but they’d likely be busy offloading and boarding the flights at that point in the evening. He did confirm though that the number published on the website for LAS is wrong by one digit. It should be +1 (702) 261-6524. Sure enough, calling that number a couple of times between 6-8pm last night went to a voicemail that was full and unable to take more messages. I called today at 3:45pm local time and was able to speak to a BA staff member who confirmed my headphones were found and I can collect at check in tomorrow.

Thanks to all who contributed to this thread with help and advice! 👍