So you're not exchanging an 'American' licence, but a this-that-or-the-other-state licence,
Yep, and that can make it very complex. I believe that one or two European countries had exchange arrangements with a few states, e.g. you could get a French license on the strength of a South Carolina license but not a Florida license, or something like that (don't quote me on the actual states).
According to the DVLA website, Canada is currently on a "must get UK license within 12 months" list (see section 3):
http://www.dvla.gov.uk/drivers/drvingb.htmThe situation regarding licenses from other EU countries is even more complex, because the rules often contradict each other! (Would I make a comment about government bureaucracy?
).
On that same DVLA page, for example, it states that EU license-holders becoming resident must exchange for a U.K. license within 3 years. The EU rules explicitly require member countries to honor a license for so long as it remains valid, which could be 10 years.
Edited for typo.