Jim,
dont use any abrasive or any chrome cleaner,

Try pure carnuba wax (with no cleaner)

next is industrial strength Amonia(sp) window cleaner.

last resort for home chemicals is MEK (used to clean paint and crud off printing press rolls.. This stuff stinks to high heaven but really works.. (use gloves as well).

Or try to find a production/ paint, polishing shop that has a dip tank of Trichlorethylne and soak them for a few minutes.