Oxy-acetylene. It can't be tight if it's liquid.
I'd probably start by using a punch and a heavy hammer to hit the edges of the nut around its circumference in the hope of breaking up the rust enough that it turns with one of the methods you already have. If that doesn't work, escalate. A length pipe over the breaker bar handle to extend it is the cheapest escalation, though you increase the chances of breaking the socket or the bar.
A sufficiently powerful impact tool will almost certainly do it, but if you have to buy it new, you might end up 500 CAD on this job anyway.