[Arran]

Peter;
The Philco (3)16X was likely a Canadian market Philco, which means that Philco Products of Canada LTD likely had the cabinet built in Canada by one of the same furniture companies that built the DeForest Crosley cabinet. The reason I was commenting of the DeForest Crosley being the most Canadian is that the Philco chassis and speaker would be more or less identical to one produced in the U.S, whilst the DeForest-Crosley sets had chassis designed and used only by Rogers, and had those spray shield tubes also made by Rogers. To be fair Rogers did source some parts from the U.S, as most Canadian companies did, but they did things in their own unique way.
Some of their larger models had variable IF bandwidth, with a mechanical linkage moving an inductor inside and out of the transformer cores. I don't think that Philco did this, though they did have squelch on some of the earlier 16 models, calling it "QAVC". Amateur radio enthusiasts were some of the early customers for the Philco 16s in part because of the five, later four bands these sets had, and the fairly reasonable price for what they are getting.
I have a chassis from a 3116X but it does not have the original speaker at all, someone put a pair of 8'' Magnavox speakers in it's place, the original would have been similar to the set you have. I never could get the thing working and put it aside, sometimes you just have to.
Regards
Arran