you can buy a barrel in Canada for the amount$$ needed to apply for an export permit, so plus the amount of the barrel cost its not worth it.
I have only ordered barrel twice because no one here in Canada has what I was looking for. look in the legalese section, NZA has put up a good tutorial and I myself have some updated info in there too.
There is some true to it that not every single thing Can't be export or vice versa. I have recently ordered a muzzle brake for a M14 and it shipped no problem, while on the same order I have added a BCM comp....BCM comp was no go. Example, regular trigger kit ( being general) can be exported as long as the manufacture is registered with the State Dept, while the same trigger kit from the same Manuf. coated with NiB may not be exported because of the coating. The rules are so twisted and complicated any average person out there will have a hard time understanding it. Best advice is to ask before you order, a quick email to Sandy is almost always 100% accurate. I am not saying we CGNers have bad infos, but get it straight from the horse mouth. Plus their rules changes every now and then and every firearm platform has their restriction.