What you're experiencing and concluding is correct. By having a higher DPI mouse, in game it will be much smoother.
The only way I can really explain it is in terms of resolution. If you take a 100x100 pixel image (IE, a really low DPI mouse) and then blow it up to 1000x1000 pixels (IE, using windows sensitivity up) you're going to get a really cruddy looking image (the jitter you're experiencing).
But if you take a 100000x100000 pixel image (IE, a really high DPI mouse) and then shrink it down (IE, using the in game sensitivity down) to 1000x1000 you're going to get a very pleasant image (smooth, half pixel movement).
For games its recommended you run as high of a DPI mouse as possible, leave windows sensitivity on the exact middle (giving you a 1x1 ratio of DPI for the game, just trust me on this) and then using the in game sensitivity adjustment to get it where you like.
Speaking of windows settings, what you're saying with short shots and long shots sounds like windows acceleration. Long story short, TURN IT OFF. You'll gain muscle memory that way, and it makes all the shots the exact same amount (1-2 inch movement or whatever you want).
Sadly, if its too high of a DPI out of game in windows, you're probably stuck changing the DPI every time you go in or out of game. I personally like my g500, allowing me on the fly to go from 400 in windows to 5200 for CSS, MW2, etc by simply clicking a dedicated button on the mouse.
Or you could just get used to the 3200 in windows, its not so bad.
And finally, to answer your question "how do people play with 400 DPI mice?" - They dont.
I hope I was able to answer all your questions. If you want to read up on how pros handle DPI and such,
my little source. Its a rather old article (I think it mentions 800 DPI as being "high" whereas I think now a days its 5200 that is "high". But the rest of the concepts are the same).