Experiences with the Silent Hektik regulator

... Conclusion: SH regulator is faulty....

I would tend to agree with that conclusion.

It would seem that Hectic ... err Hektik is an appropriate name. 

Jan - any updates here? I am considering an upgrade, looking for solutions.

I installed a Silent Hetik VR #F4123 5 step VR. Do I need a capacitor? What size? Where does it go?

The Capacitor's Positive connection goes on the Output (B) cable of the rectifier before any fuses or switches.

The Negative connection goes to the Battery/Airframe Ground.

22,000uF at 25volts is typical.  Anywhere between 20-50,000uF and 25-63volts is acceptable.  It isn't all that critical.

It will not be small, but at least smaller than a soda can.