I've been having the same issue. My problem is that I also want to use my Weber at home so removing the regulator isn't the best solution for me.
Some people have installed the following item on their camper LP tank. You would place the fitting between the LP tank and the regulator that feeds the camper. Propane Splitter.
In essence, this is splitting the LP line BEFORE the regulator.
You then need a hose to connect the new splitter to your grill. Something like this.
The fittings on either end of this hose are the same type as the 1# green LP bottles. One end gets screwed to the new fitting, the other end gets screwed to your grill.
You have now split the LP line BEFORE any regulators. The onbaord camper regulator still works for the camper and the Weber regulator still works for the grill and you didn't have to modify a thing.