by closing off the air intake hose your equalizing the air/fuel mixture which tells me that it is not getting enough fuel if that makes it run better.
by pressing the primer button your adding fuel to the mix so all this tells me the regulator is not delivering enough fuel.

take a look on the origional regulator and see that the W.P rating is on it, then look on the new one you installed and see what it is.
The W.P rating is the working pressure rating, some are different than others. But all in all since this regulator is so old i'd be willing to bet it is either the wrong pressure rating OR what others have said, it may have a bad diaphram or something. Also make sure the fuel filter isnt clogged up, we'll assume it is not since you already removed the fuel inlet line and got good squirt of raw gas from the line when you cracked the valve on the tank.