I'm not an electrical engineer - but.....it sounds like both of the "one wire" regulators are behaving the same - correct? The main lead is also the "sensor" for the regulator - and it controls the output to a fixed offset to the voltage where you are connected into the system. Your system must have very low draw at idle - and sag as the engine runs up - and the regulator is "mirroring" the sag.
The single "one wire" lead is supposed to be a large as possible to make sure the "sense" voltage is as high as possible - any drop due to resistance in the wire subtacts from the output. On mine - I ended up with a #6 fine stranded welding cable (crimped and soldered end lugs) that runs back to where the battery joins the starter solenoid. You can dummy this set-up with a single jumper cable as a test if you think the wire size is an issue - or at least rule it out.