300-600,
I'm sure many ATCOs would jump at the chance of observing simulator sessions. When Manchester Centre was operational, we often had pilots come and sit in on our TRUCE days, (Training in Unusual Circumstances And Emergencies), which was found to be beneficial. Depending on the time available, a few pilots spent time on the ATC simulator, which they found useful too.
We also had 'pilot-controller forum' evenings at a local pub, often attended by up to 100 people.
Pre 9/11, the Familiarisation Flight landscape was very different. I believe going back into the 1980s and 90s, NATS even had its own Fam-Flight section to help organise these trips. They counted as 'duty time' too, and attracted a small subsistence allowance, something which would give today's 'business managers' nightmares. Sadly, accountants do not understand the benefits of 'famil'.
A few ATCOs from my era enjoyed their cockpit trips so much, they left ATC and became pilots.
Add to this that most en-route, (and many approach) ATCOs now no longer work near major airports, and the fact that many have no interest in aviation and it is easy to see why these valuable opportunities are not taken up.
I spent many hours in jump-seats, and was always made to feel welcome, (especially by the 2 gentlemen whose company had mistakenly told them I was a CAA Flight Ops inspector).
I certainly hope your ideas come to fruition, please let us know how you get on.