The Bramley Training area is now controlled by the Defence Deer Management Group so that is definitely out of the picture.
When I was there at the School of Ammunition a very long time ago I was a member of the Game shoot and I seem to remember there were a couple of civilian members so you might get a day with them if it is still going.
There was also a lot of ground owned by the Farmer family called Dance and they certainly had Roe on their land.
Good luck.