I suggest check with White Post restorations, that is where I sent mine. Getting it rebuilt may be a good idea on an old valve even if it doesn't solve the problem, but this thing you said concerns me a little "It would be a real PITA to replace because the shop welded in a muffler near the frame where the hose is attached to the hard line." Rubber brake line close to exhaust and getting the heat may be failing, so the rubber line that you haven't replaced yet would be my first suspect.
I suggest do the switch test as in the 72 service manual here.
In my experience I did not have to disable the metering valve as they mention to do brake bleeding nor to do this test, and to bleed also did not need to use the so-called brake bleeder tool that replaces the switch and holds the pressure differential valve in the middle position. That tool is not mentioned in the manual, it is just a tool sold by aftermarket sellers and not needed, it is fiction.
The pressure differential switch does not stop flow to the front if front is leaking, nor stop flow to the rear if the rear is leaking. It simply lets you know you have a leak and should fix your brakes soon. Also it is not necessary to apply heavy pressure to the brake pedal for the test. I have observed when pressing the pedal with normal pressure that you would use for stopping, if a front bleeder is open to cause a leak, the light will come on. And if you close the front bleeder and open a rear bleeder and press the pedal, the light will go off momentarily and come back on. Close all bleeders and press the brake pedal with moderate pressure once or twice and the switch will reset and light will go off. I made these observations with a 71-72 valve recently rebuilt by White Post Restorations.