AD,
Your plan sounds fine. What I wouldn't recommend is saying "Hey, (Rocket, Spuds, Killer, etc.), its me....and I want to join your unit". NOTHING wrong with asking for XXX, then saying "Sir...I remembered your callsign but forgot your name and rank. I was told you were THE man to talk to at the XXX unit". All of that is 100% inbounds, and I'm sure the guy will appreciate your call. He might even then say "just call me XXX", which is fine. But don't walk around acting like you've known these guys your whole life and they are your buddies...that will happen later.
What I would suggest NOT doing is walking down the halls going "hey Spuds, hi Killer, what's happening Rocket etc." until you have earned that right. Generally, thats when you get back from your FTU/RTU and have gotten MR. The squadron CC is usually known by his callsign around the bar, but in more formal settings, his office, or when guests from higher HHQ are around then he goes back to "sir". Anyway...you'll figure it out based on your experience and your gaining unit when you join the team. However, one of the most UNCOMFORTABLE things to ever happen is to address someone by their tactical callsign and then get told (then or later) that it wasn't appropriate. That usually happens to everyone at least once, and you sort of plan on it never happening to you again. I'm just trying to save you the pain and embarrassment (and potentially not getting called back) by telling you to play it cool with regards to using callsigns until you know all the rules.
I'd write more, but I got to get back to ironing these flightsuits and shining these boots. As for someone gaffing off a unit deemed "petty and childish" for scoffing at people off the street who think they automatically have the right to act like "Joe Cool"...well...knock yourself out. If I had the chance to joing a fighter unit (or even a local airlift unit) when I was in my early 20s, I'd be doing everything I could to play the game by their rules...cause they have the keys to all the toys. Sounds like you are on the right track, and I wish you the best of luck.