A feeler guage that is used for gapping spark plugs should work, as for the spin speed, well you will know it when you see it, don't worry about the specs.

This model series can have a one, two or three speed motor. I am guessing that you do have the three speed motor. Based on your description I did not think the spin selection speed was an issue since even on slow spin you still should not have water in the clothes that you could wring out.

However changing the speed selection switch on the panel is something worth trying. This site (those of us who respond here are volunteer and not connected with APP sales) apparently does not have the part but you may be able to find it elsewhere.

If it is not the speed switch and the brakes are ruled out along with the other stuff you have already done then the remaining suspects are the motor, transmission and timer, and in that case I would go back to my recommendation of replacement.