Why not run the pump at your expected max rate and just measure the current? Use a spare ESC from an old plane and one of the many ammeters that are available. As the pressure builds, the current draw will most likely increase, unless the pump cavitates due to inlet or outlet restrictions. So the peak current most-likely depends on what you have for the specific system's hydraulic resistance at your desired max speed on your system. That's why one needs to be measuring what the actual current is for a specific system.

6 volts nominal should tell you that the 12.4 volts peak of a 3S LiPo is too much. You should use a 6 volt voltage regular (VR) that is also matched to the current draw (i.e. measured peak current + at least 25% margin.) You might get away with less margin. But then again you may not. Just tie your other HV components in before the VR.

Nice idea. It just will take a little bench testing on your specific system to come up with the right components. What someone else comes up with would be dependent on their specific system application.