Well, I did several missions this morning and then ranked up to Warrant Officer. For some reason, it seems to be working normally for me at the moment.
I'm really not convinced about that bar on the mission summary screen being related to anything useful to me, though - I still think it's the overall system influence level.
I'll go a step further and suggest that maybe one can achieve all ranks without ever straying much from one system - I'm starting to think that the moving around thing is all placebo.
Edit: And now Ensign. So, that's four ranks in about eight hours. All from the same system and same station. Seems about normal. Note that I didn't take any missions that didn't give medium or high rep.
Always take any charity/donation missions for Federal factions (the "give us 4,000" things), they're cheap high rep. Never bother going to go get anything. Always look to see if you can stack missions to the same other station. Always bounce between open and solo before leaving and check the bulletin board; it gives you a second set of possible missions - you may get another donation mission or something to stack. Avoid any missions that have a risk of failure. Don't take a promotion mission unless it's an easy one; if you fail it'll be a setback - just do another easy mission until an easy promotion mission pops.
If you find a system that has more than one Federal faction, you have more mission options, since you won't be taking missions for non-Federal factions.
It's all about using time wisely.
Edit again: Now Lieutenant. Still looking good...