For my gauge R&R I'm using 10 parts, 3 operators, and doing each part 4 times. Is it valid to measure each part three times and take the average and use that as an input into the Minitab gauge R&R worksheet?
It depends. If taking the average of three parts is part of your normal measurement system procedure then you may do this. It is one way of reducing measurement variation. However, it is NOT acceptable to do this if your normal process is to take a single measurement.