Hm. Tandem piston as in two pistons? Could be quite a bit of pressure pulsation and "throb" if so, and that may add to the accel's you are seeing, but more importantly puts a heck of a lot of stress/fatigue on the plumbing. Consider a triplex (3 piston) pump, as they cut the pulsations down by more than half?
Yes, I could believe 5g accelerations for a heavily loaded engine, if there is not a lot of inertial load on it, and no torque converter or similar device to absorb the torque pulsations from the motor. We had similar trouble with a 2-cylinder motor driving a positive displacement (Roots) blower, turned out that the motor had been designed and delivered to us with a lighter flywheel than "normal", we had a lot of trouble with vibrations that we finally traced to the torque "ripple" from the motor. Are you seeing any fatigue damage on the flexible elements in the coupler; is the coupler a metallic flex, or a rubber-element type? Can you put a larger flywheel on the motor and retest?