Where might one find/buy a burn/throwaway phone in general and in Canada?
Or does one have to frequent seedy neighborhoods in major urban centers to come across such?
Any recommendations?

(I have no desire or need for a regular cell phone with all its attendant "baggage" and unfathomable fee structures. I just want to be able to get one for essentially a single use — although I might use it for more if it came with lots of minutes. I quite like the idea of non-trackability which such devices offer.)

I don’t have a specific recommendation, but until someone does you might want to try Googling for ‘disposable/prepaid/no-contract’ cell phones.

My sister-in-law uses TracFone and has been pleased with it. From your post, however, it looks like you would have preferred it to be named NonTracFone!