Yes, LCBO has its hands on all things alcohol thanks to the Ontario LCA. However, that doesn't necessarily mean that all alcohol is sold through LCBO stores as things can be bought through private ordering or on consignment through agents with the LCBO restriction that you have to buy by the case.
If you wish to go this route, first thing is to call Hangar One and ask them if they sell to Ontario. If they do, then ask for the name and number of the agent. Then call and you're in business. If they don't sell, then you have to private order which I don't recommend because it can be quite costly (taxes, duties, lab tests, etc.). You can contact the LCBO for more details.
Well I guess LCBO is the only choice. Have you tried their product search feature to see whether they carry it? I know you can special order some products if they don't carry em. As for having alcohol shipped to Canada let alone Ontario its an exercise in futility. I tried to have some wine shipped over from California and it was a disaster. Perhaps some other forum member can shed some light on how to have some alcohol brought it other than LCBO.