The best advice I've ever received along these lines is "treat people as though they were already close friends." In my case, that mostly means having conversations with them about topics I actually care about, as opposed to conventional topics.
I always interpreted that piece of advice as meaning something more along the lines of "Be as enthusiastic and casual when you're hanging out with a relatively new acquaintance as you would be when you're hanging out with an old friend." This seems like decent advice, but it's very difficult for me to actually put into action, and it also seems like it would make some people very uncomfortable.
But your take on it is interesting. I'm not 100% sure I can picture it, however. Could you maybe give some sort of example of this strategy in use?
If "enthusiastic and casual" characterizes how you differentially treat your close friends, then sure, I'd say go for that. It doesn't for me, especially.
What I find differentially characterizes my relationships with close friends is that I can start a conversation with whatever has recently been on my mind, however unconventional an opening gambit, and we will mutually engage at a fairly high-bandwidth level. (And vice-versa)
E.g., I recently started a conversation (or, well, replied to "So what's up?") with "I've been thinking a l...
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.