Dampers are found in K-jet systems in higher priced cars; typically they are added to the systems to reduce pulsation noise. The adjustment screw is probably to tune the damper to the particular installation. The damper is probably not a cause of the problem.

A change that you can make as a test is to disable the push valve section of the fuel pressure regulator (FPR). There are two o-rings in the FPR; the smaller o-ring is on the push valve. Remove it. Without the push valve o-ring the control pressure circuit will be open to the return line when the engine is shut off.