I usually find there is one "Genealogy Nerd" in every branch of the tree. You just have to luck into the correct person. I always approach it by outlining the direct connection if I now it. i.e. draw a line from me to this person exactly how we're related. To the muggles who aren't into genealogy, I imagine it comes off kind of "stalkerish". I do find that it is usually worth taking the chance as I have connected with some very interesting people along the way. The more it is personalized, the less you sound like the Nigerian Prince who has left you millions of dollars.
I would do one email address at a time, maybe trying a second one if there is no response from the first. I've never gone the snail mail route.
Scott P. Dann