Poopdeckpappy,
My gut feeling on this is that the higher pressure/volume
pump will not solve the pulsing (might make it worse). Normally the problem you are having is addressed by adding the "expansion" tank mentioned above.
If you are having trouble locating an "expansion" tank, I thought I'd mention that in marine applications they are generally referred to as "accumulator" tanks. They are a fairly common component of domestic fresh water systems aboard sail and powerboats.