Yeah, the latter half of your note is right—the biggest problem is that it's not a question of comparing current costs to what costs would look like if they moved toward a single-payer system; the real hurdle would be the cost associated with getting to a system of nationalized healthcare. In the US, the government doesn't itself administer healthcare as is the case with Canadian provinces; they'd literally be setting up their system from scratch, and they'd have to figure out how to administer it to 330 million people, as opposed to 35 million people.
Now, even if we were to completely set aside the costs associated with migrating to a single-payer system, it's reasonable to predict that costs would decrease given, as you noted, that the only industrialized nation without a single-payer healthcare spends more on it than any other country in the world. In other words, their way doesn't work as well as ours (or that of any other industrialized country).