I agree that visits for both sides are really worthwhile, it's been a long time since I saw a pilot at LACC. NATS apparently have agreements in place with certain airlines for famils and (I believe it's called) STAC sim training. EZY, BAW, and BEE spring to mind. I don't think MON are part of our agreement, but I know they've been excellent in the past helping to arrange famils for ATCOs. Our booking process for has recently changed too and is unnecessarily complicated, which doesn't help encouraging people to take them up. Spaces also seem to be really limited unfortunately, whereas before you could submit requests for dates/routes. Using your own initiative and arranging one yourself is apparently frowned upon!
I agree with Zooker(!), I'm not sure office staff appreciate how valuable these are for us. How can we adapt the way we control if we never get chance to speak to flight crews?! I think it should be part of our licensing that we go on a fam flight even once every 24 months or so. There must be a lot of pilots out there that've never visited an ATC centre too. In terms of your videos, NATS Safety department would be the best place to send them.