I think you have a great idea and your request is respectful and well thought out - I only have 2 suggestions (and remember, these are just my personal opinions).
1. Just a gramatical thing - where you are talking about people who detect, call them dectectorists, not detectors - detectors are what you use
2. I think if I were you, I would keep the letter on more of a personal basis and tell them what kind of hunter you are (you take garbage and trash away with you, you return things that can be traced to an owner etc...). There are alot of us out there who are wonderful at those kinds of things, but there are also folks who would go in there and leave large crater size holes with all the trash tossed on top and you don't want to be speaking for them.
The sad thing in these situations is that all it takes is one bad apple to spoil the pie for everyone - so if they let you out there, they'll have to let everyone who asks go out there and the first time someone leaves holes everywhere and trash all over, it'll be the end for everyone.
That said, I personally think you have an excellent idea and I'd love to hear what kind of response you get from them and hopefully if you're able to hunt, you'll post your many finds!!
Good luck