You need to contact the Export Desk at Brownell's.
Phone. Ordering online gets you the standard "We Don't Export" message. They do. It's a slow process. IF the maker of the barrel is registered to Export!
It's a slow gratification process. Like planting acorns and waiting to be able to sit in the shade of the tree slow.
If it can be bought from one of the dealers here in Canada, it's going to be faster by a long shot, and like as not, about the same end cost, or cheaper, if you factor in paying an Importer.
Figure it this way. The dealer that imports it, sits down and does the paperwork on their whole shipment, once. It takes time. The Importer that you hire is charging you the same time to sit down and do that same paperwork, once. The dealer can amortize his time over the whole shipment. Or you can do the paperwork and sit and wait. IIRC, no charge at this end for the Import Cert needed, fill it out online, and wait.
Follow the directions, fill out the forms, send them and wait.
Then wait some more.

starting to see the pattern?
Start with the phone call, see what the final price is after fees and shipping, then see if it' worth it to you.
Have fun! Order some paper catalogs while you are at it! Good outhouse reading material.
Cheers
Trev