Here is an update: I'm happy to say that I finally got the ST4000+ performing perfectly! This includes basic motoring --AND-- under sail. I am absolutely amazed how well it performed under a 15 knot wind while sailing close hauled. How did I fix it?
Well, for one thing, I discovered the "Catalina cocktail", which apparently also works for Hunters as well [grin].
The "Catalina Cocktail" suggested by Raymarine is:
Rudder Gain 2, Response 2, Auto trim 2, Drive type 2 (hydraulic).
I tried that, which vastly improved the tracking (with/without GPS), however it would STILL get out of whack on occasion, (little S turns, over-correcting to large S turns). It didn't happen THAT often [grin]. I'm my mind, the ST4000+ was "good enough".
I then (later) I discovered this website, which was really a guy who managed to create his own rudder transducer using an old transducer made by VDO.
http://northernlight.vermontficks.org/rudder_sensor.html
I read this, only because I like this sort of clever creative thing. But the thing the caught my attention was this comment he made:
"Without the rudder reference transducer, the ST4000+ autopilot display appears as follows."
"After installation of the rudder reference transducer, each time power is applied the autopilot recognizes the presence of the transducer and displays the rudder bar at the lower edge of the screen."
I thought for sure my rudder transducer was being recognized by my ST4000+, but I was flat WRONG! I thought this because in "Auto" mode, the curved rudder bar was there on the bottom of the display.
In STANDBY, the ST4000+ *MUST* display the rudder bar, but mine didn't! That was the "A-Ha" moment. Suddenly, this link became much more credible and I totally followed what this guy said, and followed the procedure he outlined to get the ST4000+ to "correctly" recognize the rudder transducer.
After this, along with the "Catalina cocktail" settings the performance of the ST4000+ was simply astounding.
Folks, the ST4000+ absolutely *NEEDS* the rudder transducer. It is really NOT an "optional" item. You need to trust your autopilot, and not accept that "for the most part", it performs well but "occasionally" it goes out of whack... NO NO.
It now steers the boat just as good as human, motoring or sailing.
Next time you power on the ST4000+, check to make sure the rudder bar is there in STANDBY.