I'm going to go ahead and agree with what Cheesehawk said.
Especially the gear and car analogy is the one i use too whenever explaining CEM to someone
In the sense, if you want to cruise at high speed keep it around 2000-22000 RPM.
Lowering the RPM confuses a lot of people because they think that they somehow lower their available engine power. What really happens is that the RPM lowers because the prop blade angle of attack increases: more resistance but also more pull.
Long story short, you will need to fiddle with the pitch control all day long. Don't expect to set it around 2300 as an all-around happy medium, leave it there and attain top performance.
Once again, think of gears in a car. Lower gears are useful for braking by loading the transmission system if you take your foot off the gas pedal, for getting a sharper, more lively response from the engine, going uphill or going downhill at slower speeds. What is the hallmark of a lower car gear? Higher RPM for the same speed. That's your mnemonic rule right there, whatever you want to do something that would have you down-shifting in a car, use higher RPM in the aircraft
In a similar fashion, higher gears give you less actual "pull" in tricky situations and a slower engine response but they are great for attaining higher speeds and still be great for fuel economy. Again, higher gears means lower RPM for a given throttle setting and speed so that's your cue...whenever you want to do something that would have you up-shifting in a car, lower your RPM in the aircraft.
As for why the prop-pitch mechanism is slow, maybe it's partially dependent on the amount of airflow, the amount of throttle used and the airspeed. I have found that prop pitch changes are faster if i put some load on the engine or i'm going faster. Another way to speed it up a bit is to deliberately overshoot your intended setting in order to "kick-start" it so to speak, then bring it back where you want it.
Alternatively, fly a lot of free flights and get used to the sound of the engine. This way you can tune it by ear while looking outside the cockpit, instead of having to bury your head in the panel and check up on things in the middle of a dogfight.
I didn't expect it, but i actually find the little clock displays that indicate prop pitch very useful. They are at the upper part of the panel in both the 109 and 110 and are easy to keep in view. Between getting used to the engine sounds and noting down what my prop pitch settings are during certain scenarios, i can now fly without looking at the tachometer all the time.
This is also helpful to "change gears" and ties in with the way to use the entire system. These pitch changes are manually commanded, so it's like having a myriad of fixed pitch propellers. Well, every fixed pitch prop will maintain a certain RPM only under specific airspeed and throttle conditions. I hope i'm making sense here, i don't know how else to explain it in a simpler manner
So, back on the topic of "shifting gears" in our plane, you have to take into account the aforementioned delay and plan a bit ahead.
For example, you just made a diving pass on some bombers and are about to pull up into an immelman in order to set up your next pass. Don't wait until you start pointing the nose up and the RPM drops, advance the pitch as the nose is still coming around to take advantage of the fact that you will get extra RPM as you are still diving and this will also help turn the blades to their new angle.
All in all, it's just like shifting gears but with a slight built-in delay. And in that sense, going flat out on full RPM will certainly not give you top speed.
I use 2500RPM when i want to climb or to accelerate, then i drop it back to 2100-2200 or so for level flight and dives.
This might be a bit confusing initially but due to the way Fw-190As were in the stock IL2 i got used to flying with manual pitch a long time ago (it performed better than with the auto system).
To sum up:
a) Remember that your RPM power band is from 2000 to 2500 RPM
b) Use the low part of the power band for top speed, cruise and accelerating in dives and accelerating in level flight when your airspeed is considered high (ie, sufficiently above cruise and closer to max).
It's like going from 5th gear to 6th, it will slowly give you that extra 30km/h in your car, if you go from 5th to 4th however you won't be able to get that top speed since even though 4th accelerates better overall the top speed range is out of its capability
c) Use the high part of the power band for top acceleration, especially from a slow starting speed, and fast engine response to throttle changes. This goes for throttle increase and decrease alike, which is why fine pitch is used in take-off/landing and for keeping formation. There's a reason why wingmen usually burn more fuel than the leader, they run somewhat higher RPM
d) When you know you will change attitude and/or airspeed due to maneuvers, anticipate the needed changes in pitch and start them a bit earlier. If you see a hill or a truck you want to overtake ahead on the road and you know you are going too slow for your 5th to get you through it, you downshift to 4th in preparation for it. If you know you'll zoom back up after a diving attack, start increasing your RPM just as you stop pressing the fire button.
You might temporarily over-rev a bit but it's not sufficient to kill or even damage the engine. My only worry in such a case is that i might actually be lowering my airspeed prematurely by going to a "lower gear", the engine can take brief bursts of 2600-2700 RPM just fine. The key word here is brief, i routinely overshoot into the 2600 RPM range when pulling out from dives but it only lasts a few seconds (probably less than 5).
Hope it helps somewhat