Unhook the carb inlet and route a line back to the tank. Let the pump run for a while measuring voltage and pressure at the regulator. You should have steady regulated pressure, if not work backwards till you find the problem. What pressure are you trying to run at? I would start at 4 psi and see if it steadies out, 4 will be plenty of pressure and the standard Holley regulator should be quite happy there. The Blue pump should also be happy at 4 psi.
Any restriction before the pump will cause a low pressure, not a high spike. I suspect the regulator in the pump might be sticking or the regulator #12-803 is acting up. What spring is installed in it? The repair kits include a heavy and light spring, don't remember what pressure range they are for, but install the lightest one if available. Is the tank vented? Try running with the fill cap loose.
To eliminate any voltage problems, add a 40/50 amp Bosch relay pulling power right off the battery terminals. Run a power and ground and use the existing wires to trigger the relay. Use heavy 12 gauge wires, it will increase the life of the pump motor and reduce any weak circuits.
If all else fails, you can add a return line off the regulator. Plumb the carb to the pump side and add the return line to the regulated side. The carb will only see the regulated pressure and the tank will get the unused fuel. This is a way to keep the pump cooler and insure full flow to the carb. A lot of alcohol burning race engines use this to method.
Joe