I'd try some petrol. The paint should be an enamel anyway but just to be sure; try rubbing a petrol soaked cloth on an out of sight place such as the back casing.
be careful, washer paint is not enamel & some petroleum based products can damage both plastics and paintwork (id use petrol lighter fuel) and yes i know it sound contradictory, but this does work with sticky labels etc without causing damage.
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