You may be correct in diagnosing your problem, however I believe I know what the problem really is. It is most likely not your regulator, but a safety feature built into the valve on the tank. If you are using 1 lb cylinders, then I stand corrected, however if you use a hose to connect to a 20 lb cylinder it is the safety built into the tank valve. I experienced just exactly the same symptoms you describe after I tried to light my grill the second time, first time was fine, from then on I cussed that grill and never could get it to light more than a feeble flame. I took the tank into a Hardware store to see if it was empty, luckily for me he was reputable and just weighed the tank and it showed full. He told me about the built in check valve in the head.
Solution: You must keep the burner valves turned off once the hose is connected to the tank, then just barely crack the tank valve and let it seep into the hose very slowly until full pressure in the tank is reached in the hose, that will release the check valve in the valve head. Now you can go ahead and light, you may have to repeat a couple of times. I learned that once pressure was equal, I never close the tank valve unless I am going to break the grill down for transport.
i normally walk away and do something else as the hose come up to pressure. It takes a while.