A motor can draw several times the name plate amps while starting and even an unloaded compressor takes a good effort to start. Some literature suggest in the neighborhood of 5 or 7 times name plate amps!
I'd solve the problem with a motor starter rated for the size/amps of your motor.
May be able to clean the points on the old pressure switch and use it with success for "pilot duty" controlling the new motor starter.
Also, might be worth checking the condition of the starting capacitors (not sure how) but I can imagine if they were not doing their job it'd have serious starting amps.
Grigg
