Just some thoughts. Seems you've discounted Brunters so some other possibles. I did an MSE academy day at Upper Heyford years ago, no idea if the airfield track is still available. We did that training day at Alconbury with Ben - although I don't recall it being that smooth. Can Plans get you out at Dunsfold?
I had thought about Alconbury I would need to find out how it has deteriorated over time.
PS sounds like a good idea