Capacitors in particular electrolytic are unpredictable as to failure. Electrolytic do worse when sitting for a long time and then applying full voltage due to chemical changes that occur with lack of use. Sometimes older electrolytic can be reformed or conditioned by slowly applying power in stepped increments. The other factor that causes rapid deterioration/failure of electrolytic capacitors is quick on/off cycling which quickly overheats the capacitor or a sticking start switch. Electrolytic capacitors are used in motor start applications due to their higher charge density for the size, as opposed to other types of capacitors which would be much bigger for the same uF/V rating.
As far as replacement, I have helped a few people with G4003 replace the start capacitor, the ones I have seen required cutting the wires to remove the capacitor. One issue is finding a better quality one that will fit in the space, the asian ones always seem to be smaller for the same uF/V size. You can check online at various electronic/motor suppliers, I often check those for pool pumps or for AC systems, as they must take more extreme temperatures (pool pump ones tend to be smaller). I think you will have an issue size wise going to a higher voltage, but check around. Also get one which has a higher temperature rating, so something like 105C instead of 85C, it will be more likely to handle the heat generated from cycling on/off. Most of these motor type electrolytic's that are decent seem to come from Mexico these days.
