Bottom line adjustable regulators are not at all meant for cooking appliances (well turkey fryers sure) but not things with a "cooktop" or "grill/griddle top". They're meant for appliances using very high volumes of LP at MUCH MUCH higher pressures than a normal cooking appliance. I.E., ready heaters, large deep fryers, what have you. Grills are designed to use TOPS 11"WC. And those adjustable ones cannot hold pressures that low steadily. Because it is not what they're meant to do.
I didn't even want to go at the GrillGrates as they're not a great idea especially used in this manner. Seems the grill has a "problem" and the wise thing to do is fix the problem. I've cooked on many Q2xxx and have never found them to be "heat lacking" in the middle. I've actually found them dead even across the grates. Again here too, only if the proper grates are used. With sufficient mass, the deflectors built in for the burners.
This sounds like a disaster waiting for a place to happen