I heartily agree that direct contact is the best way to educate each group about the other's problems. However, no one route experience or ATC visit will highlight all the problems that exist for each side of the equation, so question-and-answer sessions like this one can fill in many of the gaps.
I believe that my airline has an ATC liaison pilot who deals with air experience, though I know little more than that. I will try to find out more; the latest DoT rules make it explicitly clear that you ATC peeps are 'permitted personnel' on UK flight decks, so there is no regulatory reason why you shouldn't come with us - we just have to persuade the bean counters that we can afford the hotel rooms for you (not to mention the beers, food, beers, entertainment and - oh yes - beers).
Scroggs