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I am not aware of a capacitor that would correct this... if the contacts stick, anything parallel would not stop current from flowing. If your watts are correct, it sounds like a true failure. I suppose one could get creative and place a second thermostat (set for a higher setting) in series with the other one. This way, if either opened, the circuit would be shut down. There are fusible links, but finding one to handle that current, placed in the right place and set to trip at the right temperature could be used, but thats a stretch. I agree your situation is scary.
Personally I would replace it if you can. If it stuck before, It may stick again.