Ok I had very similar problems when I first started running Dresden sense i had never run a fate system before. Here is what I did:
-First I made a cheat sheet with all the characters and and all their aspects on it.
-Then I promoted players self compelling... I even allowed multi-compels in situations where the compel applies to more then 1 aspect. Only problem was to many fate points started to flow so I also put a rule in that you could not compel your aspects more then once per scene. This limited the flow of fate points to a max of 7 per scene but usually more like 4-5.
-Next I started awarding fate points whenever players do things that are particularly inventive, heroic, or funny... i don't mean your character told a funny joke. More along the idea of your character was fighting an ogre and you took off running from the fight screaming like a little girl, to make the ogre think you're all super weak, and when he caught you, you shoved your grenade down the gullet of the ogre and lept away from him letting the internal explosion knock him out. Then you stand over him and declare, "Be careful what you eat, heartburn is a killer." Maybe something less cheesy lol. Other examples would be self sacrifice moves to save a party member, a plan that turns an encounter i have designed that should have been a slobberknocker into a easy situation, ect.
-I also allow my characters to make declarations that they have gotten to know another players character well enough to have figured out some of their aspects. If they seceded the appropriate roll then they learn some aspects and have the ability to compel each other by tagging the companions aspect and passing them a fate point. This works beautifully when the party wants to do a certain course of action but one player is holding out even though he has an aspect that would push him in that direction. By the players compelling each other vs me doing it, it gives the players the feeling that they have a certain amount of control with each other... like they can appeal to what they know of each other to convince one another to help each other. I find that better then the feeling that the world is out of your control because the god figure of the game (GM) tells you its gonna happen and hands you a fate point.
After doing these things I found that my characters have a steady flow of fate points and tend to hover between 3-6 in the bank at almost all times. Due to that they have started framing the scene more and spending them to do more daring heroic moves. I think it has made my games much more interesting.