A restrictor in the gas line is always a good idea for reliable first time starts.

You should be able to tighten down the screws of the pump cover, the clearance between the cover and the cogs is what makes the difference in how well/efficiently it pumps, as these two screws also attach to the motor then there may be a alignment difference pushing sideways on the shaft(drive cog) out of the motor.
I would remove screws and look into holes with a torch see if the pump holes are lining up with the holes (threads) in the motor, if not then a slight enlargement of the holes in the pump body might help the screw line up better.
Another fine tune would be to shim between the motor and pump with wafer thin plastic washers, you may find that shimming it out slightly or just one side will cure the problem.