Just concentrate on getting easy miles in. If you cant talk to your pals - its too fast for you. Recording X miles in Y minutes sounds like you're getting competitive with yourself. Just rack up the miles - they are your friend.
I think I'd just go with what parkrun want. They dont want to p*ss off the NT and risk their other runs.
Hopefully NT will get a new manager at that location and they may see the light.
As has been pointed out - getting the cafe up and running for cake and coffee from 9.30 would be a money earner for them after all.