Yes, in the end, "elbow grease" (or, to be more precise, the repeated application of several fingernails, until they wore out !) removed far more gunge than most of my chemical treatments. I also learned, as a part of this exercise, that I had been putting all sorts of things into the dishwasher that were not supposed to go in there, according to their manuals : the pan and lid of the deep-fat fryer, the lid of the pressure cooker, ... Ah well, they seem to have survived, but it will be more elbow grease and less dish washering in the future !
** Phil.