It's an awkward one mate. I am lucky enough to live in the middle of it all and grew up with farmers so they know me of old.
I actually have around 500 acres that I have yet to set foot on, and I have had the land for three months ( I picked that up at a funeral believe it or not)
Its all about trust at the end of the day, and farmers are bloody neurotic at the best of times.
Even now years on I am scared that one particular farmer (and friend) will find out about an "incident" I had in a grave yard with one of his sisters some years back and kick me off (well you know what happens when your full of cider)
Join a cheap syndicate and get in those circles, mix with shooters and maybe join a shooting club, make some contact with other shooters, no matter what form of hunting or shooting they do.
Go picking up or beating,.. anything!
Get your face seen, but don't muscle in in anyones shooting, as you will become very unpopular real fast.
It has happened to people on this site when they tried to help someone.
I have never had to write letters, but I am not sure that I would go that way. Its easy to bin it, and letters don't show your true character
Offer professional services in exchange for shooting rights,one of my farmers sons is getting married in May and I am playing his wedding night for him, needless to say there will be stacks of other farmers there that night and I will circulate among them. (not their sisters)
There is no easy way, its hard to find shooting and bloody eay to lose it.
(Thats before a syndicate comes along and buys it from under your feet)
Hope this helps, and good luck