Short and sweet, that Gloria is a beautiful piece of machinery. Please be very careful if you plan to clean that chrome. Using bronze wool is no guarantee that you will not ruin it. I have used just about everything on old chrome that exists out there. One thing you want to be very careful of is that some old chrome, particularly French and British will lift off like erasing a pencil mark on paper if you are not careful. It is very thin.
Any such cleaning should take place on a chrome spot that is not immediately visible. Somewhere under the bicycle, inside a dropout or anywhere that is not immediately obvious. I would start with a very small area and try what you will use very slowly and check your work very frequently. Bronze wool may sound innocent enought but I have seen it remove old chrome very quickly. Frankly, I would take and old cotton cloth, put some oil on it and rub an area slowly and see if that cleans off some of the dirt and crud. That chrome looks very fragile to me and once gone it is gone for good. Products that I have used that I like for chrome. No. 7 pink chrome polish although it seems very hard to find any longer. Soft pencil eraser and for chrome that is a bit more sturdy than this, 0000 steel wool with a dab of No.7 rubbing in very light small tight circles and checking your work frequently.
Good luck
Ray Homiski
Elizabeth, NJ USA