I've got the Holley "Blue" pump and I had to add extra rubber insulation to the mounting bracket to quiet it down to a degree. These are rotary vane pumps and it's their nature to be noisey.
A quieter pump is the georotor type. Its design is similar to the Ford oil pump. They are usually a bit more expensive than the vane pumps, but it may be worth it to keep your sanity. I, personally am about sick of hearing mine. I'm seriously considering going to a high volume mechanical pump rather than the added expense of a georotor design, but that's just me.
The sound of my pump will change with the amount of fuel in the tank and when the fuel sloshes around in the tank. If you are using a fuel pressure regulator that doesn't have its own return line, this will contribute to the excessive noise.
In your situation with the symptoms that you describe, could be a bad motor bearing or a binding in the pump itself. This will make the motor's armature harder to turn and cause a higher than normal amperage drain which may be causing the fluxuations in the electrical system.
You can check the amperage draw of the pump with a multimeter to see if it is drawing more than the spec draw. I'm using 12 gauge wire for my electrical leads. Wire that is too small will contribute to an excessive amperage draw, especially if the wire is running the length of the car. My battery is trunk mounted and my pump is wired directly to the battery through a relay that is controlled by an oil pressure switch mounted to the engine.
I also have an inertia switch installed in the pump's power lead from the battery. This switch cuts off power if subjected to impact. The switch can be found on any fuel injected Ford, usually located in the trunk area, if you source one from a salvage yard.
You didn't mention how old your pump is, but I found that mine quieted down only slightly after a period of time. The vanes in the pump seated. It still makes enough noise to drive me nuts, though.
The first thing that I would do before pulling off the pump is to check the amperage draw. If it's higher than it's supposed to be, something is binding up or there is a restriction in the inlet side of the pump. You say that the electrical connections are good, right?