Stopping the flow of the coolant to the heater core is the function of the monovalve on the 560SL. It actually regulates the flow by switching on and off during normal operation. When off, full flow is achieved. When on, flow is shut off. It grounds out to change states. Sounds like you still have an issue with the valve. According to my CD manual (section 83-603), if you move the dial to min and press the total ventilation button (second from the left), there should be no hot air from the ducts and the heater core (exchanger) should be cold. The manual basically says if it is hot, either the monovalve is bad or the circuit controlling it is bad (I'd bet on the valve). It does say to check to see if "positive and negative are available on double coupler", but also warns of a possible short circuit, and I assume damage to the electronics if the wires are touched or shorted out. It also says to check for proper connection and bending of the connector at the valve which may not be making contact.

So yes, your idea is valid and there is a provision for this in the system, the monovalve, that apparently isn't working. Either the one you replaced is faulty, you have a bad connection somwhere, a bad fuse, or a problem with the pushbutton unit or climate control computer. You can always add the manual valve, but it will affect the climate temp control from what I read.

I recently retrofitted my 560SL to R-134a. I was amazed that with only half the charge the A/C was cold. So I know the A/C system in the 560SL works very well.