Coincidentally, there's another watch being discussed in another topic/thread. It too has a case that has the appearance of solid gold, i.e., no wear-throughs, inner case engraving more common in solid cases, a thin case band, etc. While I don't see your case as having "heavy" engraving (It's somewhat subjective and relative.), it does have what is called Jurgensen lips. In honesty, I don't recall ever seeing them on a gold-filled case, but I haven't seen all cases.
I'll join Steven Thornberry in asking for an image of the movement. Personally, I doubt that the case is original to the watch, but there is some chance that it was a new replacement case, although I doubt that too. It would be nice to see that movement image to check for clues of the case having housed another movement in its life.
FWIW, I really like the dial on your watch. And the 162 is a very nice grade to own. I think it's the cats PJ's for 16s Elgins. Congrat's.