I think a good start would be to make an appearance in person, especially if no one is returning your calls/emails. Not only will this show that you are a bit more serious, but it is also harder to ignore a live person than it is to not answer an email or call you back.
You probably won't get a JSUPT slot without visiting at least a couple times anyway, so you might as well start now!
I realize you can't do this for every unit without knowing whether or not they are convening UPT boards, but it sounds like this is the one you are serious about so I say coordinate with your acquaintance, drop by and introduce yourself.