This will be no problem with those wire sizes.
160’ of copper#8 with 28 amps is 2.58%
200’ of aluminum #2 will be 2.13%
So a total voltage drop of 4.71% this is below the NEC recommended 5%.
Note the actual voltage drop at startup will be higher but a standard water pump should be fine with class 10 overloads (standard fuses and breakers are usually ~ class ...
Pump motors usually spin fairly easily. My guess is the bearing seals have failed and the extra drag is causing the motor to buzz or hum.
It is possible you can disable and get to the bearings on the shaft. It is normally the output shaft bearing that fails.
A high quality double sealed bearing for a small pump like that will normally be only a few dollars, ...