I know exactly what you're talking about. There are a lot of good comments here. The ones that I've figured out are the most important are small rudder movements, good throttle control, and good shifting. You are absolutely right that you are stalling out the rudder when it's hard over.
I've found that keeping the rudder centered up, then going with 1/4 to 1/2 rudder, followed by a burst of throttle, say 1600-1800 RPM, then backing down to a high idle, or going to neutral. This gets a quick shot of flow across the rudder for corrections, but not so much that you start going every which way. It also seems to me that about the time you are noticeably turning, get the rudder back to center, once she starts going she doesn't want to stop. I think of the prop/rudder in terms of a bow thruster and give it little gooses here and there.
All that said, my batting average is probably 40-60% on getting where I want to go on the first shot.
S/V ARGO - Pacific Seacraft 37 Hull No. 309