Things id do if it were me... (which it was)
1. Definitely try to see if a CLI is in your cards with Navy Fed.... you *should* be able to get one... Esp if youve had it for over a year which is what i think you were saying...
2. Go app for credit scorecard to get a free FICO score... ALso wanting to get you on discovers radar....(And possibly save yourself one HP instead of two on app.. Not guarenteed however)
3. Id wait a month for either the CLI from Navy if successful AND paying a bit more down on the Navy card would be very useful....
4. Im betting that discover offers you a card via CS but even if not.. try the prequalify... (not the most reliable but predict youlll get a small range and/or a particular APR) You probably could cold app sucessfully but would like to see roughly what they think of you in targeted offers... May not get a huge CL on the first pass with them. but dont sweat it.. Then again you should do reasonably well...
5. App for discover and look around for another card... one of Amex's revolvers is a good possibility or even something else.. the third card will likely cause a temporary dip in your score... Dont sweat it.. youll be alright... If your thinking chase.. id try to get your Navy up a little higher and or wait for discover... With me.. chase intentionally tried to one up my CU card.. which was 5000$ at the time... but not by much... It hasnt grown since...
6. Try to prequalify and app for that third card... whatever you decided......
7. Sit back and garden for awhile... and if that self-lender loan is ending/ended think of an Alliant Secured Share loan in its place.. Pretty great rates for just savings too but they dont shorten the loan perioud with prepaying up front.... there are threads on this...
Your credit is great.. but really need another card or two more to strengthen it then to raise it... I ran into the same problem... Youll notice some small dips but you will get them back.. honest.....
-J
As joltdude says, Discover's prequal tool isn't very reliable. But with the loans and the current card, I think your chances are likely OK.
Capital One, AMEX, and Chase have very reliable prequal tools, particularly if they give you a definite APR rather than a wide range. I think Chase is a tossup at this point, but you might be good for AMEX. I would think your chances would be excellent for a Capital One Quicksilver.
Lots of good ideas in this thread. 
Navy gives out cli every 6 months. Go to the navy thread to strategize when and how to do it. It's a hard pull. Also I recommend Penfed who has been known to give high limits right off the bat with scores like yours. It's $22 to join and there's another thread with step by step help. Penfed pulls Eq fico 9. Is 770 your Navy score ? They also pull EQ9.
