Barrels are major firearms components. Each shipment of major components needs its own export licence from the State Department under ITAR. Brownells, for instance, charges $250 now for this process, so something like a barrel is going to double in price before the exchange.
Non-major parts fall under an exemption in ITAR where each shipment under $500 (wholesale) to Canada doesn't need its own licence.
In all cases, licences and exemptions ONLY apply to companies registered with the State Department as exporters, *and* the manufacturers of the parts must also be registered. This costs money for the companies, and there are record-keeping requirements.