Archeologists have begun cleaning carbon deposits off of old paintings, with pulses from a laser. could the same work for the hydrocarbon deposits?
it would seem to be optimal: http://www.sciencedirect.com/science/article/pii/S0022311510004241
Also, copper dissolves in hot concentrated sulfuric acid, which shouldn’t harm glass, but definitely will harm steel (my stainless steel sink was stained, that way).
Can the glass be removed from the supporting steel, for cleaning?