Motor Poles and Maximum Efficiency

I believe that you will want the four pole 20 HP motor just for the simple fact that you will not be exceeding any of the drive characteristics. To he11 with the theoretical efficiencies.

In the case of the 4 pole (1800 RPM)the operating speed will be 70% of the rated speed at 60 Hz, whereas the operating speed of the 6 pole will be 6% above the rated speed (1200 RPM @ 60 HZ)

On general principles, expecting any component to operate above any stated parameter will bite you somewhere, somehow. It maybe premature bearing failure, it maybe that 1272 RPM is not possible at all with that motor under load. (Oh it's been a long time since I've used anything but a stepping motor, but I think that efficiencies rise when one lowers the drive frequency from normal operations and drops dramatically when increasing the frequency above operating points, too.)

I am also suspicious of the stated constant torque load. I suspect that getting this displacement pump to start moving will require more torque than to maintain motion. This higher torque to start motion also favors the lower pole motor.

I'd look at nameplate amp draw and service factor. At 6% over you may not be close to FLA. Then, there's the service factor, which I have used in the past without problems. These were 5 HP centrifugal pumps. Gotta eat.

I do agree with redfred

You have a positive displ. pump pumping something at 1271 rpm, requiring 9.2, say 10 hp to do so. You do not mention a variable pumpage output, which should have a high-low limit in Q and rpm. (Q=output volume in time, like gallons/minute (gpm) or other) But you do mention a constant torque. I assume therefore, that your Q is constant, at a constant rpm, needing 10 hp to do so. So the question arises why do you need a VFD in the first place. And why a 15-20 hp motor when you need 10 hp. Your motor should run at about 90% loading. Then you get the best power factor and best efficiency. Surely you don't need a VFD to reduce pump shaft speed from nominal to 1270 rpm. There are excellent speed reducers on the market, costing much less than VFD and much less troublesome. A 6 pole motor will run at 1200 rpm and a 4 pole at 1800 rpm, which is the industry standard. At 1200 rpm your Q will be a bit less than what you get with 1271. Can you live with that? If you can, go for it. Then a direct shaft to shaft drive will do the job just fine. No VFD, no speed reducers. And match your motor hp to your need as closely as possible.