Mysterious. If the new pressure switch still fails to cut out at 60 pounds...either it is a bad switch, or the switch is not the problem.
Are you spraying a wettable or flowable formulation? Potentially something with could plug small openings. Do you have dirt or residue in the tank? Do you have a screen or intake filter?
Why not get a bypass valve and let the excess flow back into the tank?
Or get a new pump--and be done with it.