With an exhaust valve on the diaphragm, think about how you are going to clear a flooded mouthpiece. Where is the water going to go? You will not be able to exhale all the water out and at some point you may inhale some water.
The Northill Airlung has a DSV (Dive surface Valve) mouthpiece valve to keep the breathing loop dry, similar to a re-breather. You are supposed to close the mouthpiece DSV valve before you take the mouthpiece out of the mouth. This minimizes any water in the loop.
I don’t know much about the Northhill, but using a conventional mouthpiece doesn’t sound like a good idea if you ever want to take the mouthpiece out of your mouth. I think you will have a real hard time with a fully flooded mouthpiece.
Here are some good pictures of a Northill for those who haven’t seen one:
The Northill Airlung was made of
The only other double hose regulator that I am aware of having a diaphragm mounted exhaust was the Dacor, but it also had two diaphragms to separate the dry chamber from the wet chamber.
There have been several single hose regulators with exhaust mounted on the diaphragm, but those are intentionally wet chambers. The chambers are small and easy to clear any water out of them. In a double hose you don’t only have a large chamber, but two long large hoses that would need clearing.