That's a sweet looking panel.
I honestly don't recall a situation where a regulator didn't provide at least some
throughput. I've seen plenty where a regulator wouldn't shut off, or crept up in pressure, or had the PRV valve go off, etc.
My thought was perhaps you have a stuck check valve on the bad regulator. Unfortunately the site doesn't mention if the shut-offs have integrated check valves. And you can't tell from the picture.
You can find out by disconnecting the tubing from the barb, opening the valve all the way (shut off the tank first!
) and shine a light up the bore of the barb to see if there's a check valve ball, or if you just see the ball valve (twist the valve handle to check what you're seeing).