Waiting is best, especially since you just got some cards.
With that said, I got a 1K SL on the cash Rewards (at 14.something APR) a few weeks after I first joined Navy. My most recent CC approval was 4 months before that. Four new cards in the past 7 months (I was rebuilding from zero cards!). I had plenty of other things going against me but they still gave me my cash Rewards card.
But again, since you just got these other new cards, it sure doesn't hurt to wait. Pay a lot of attention to your Navy account (direct deposit, yadda yadda) and give it another two months! Congrats! 
Navy loves DD. Set up DD with Navy, even partial, if you can do it and pay out of it, transfer funds or use their checking, I'm sure you can figure out what best would work for you to have DD with them. Keep holding off on apps for a while then when you're comfortable, apply for Chase if that's what your most desired new card is. After that, NFCU will be comfortable with your DD and will probably be asking you to get a card. But wait 6 months after Chase acct, and ask Navy for a card, and if you like, a LOC attached to checking or second card. I'm sure you'll be happy with your results. If not, wait 6 statements and ask them for a CLI, ask for max and if your scores are still high, NFCU will be fairly generous. NFCU really wants to be your main bank, if not your only bank, they do their best to make it happen. I know it seems like a long path, but you'll have what you were wanting and be in with the best CU you could ever join.
