Alaska doesn’t fly to Montreal, so you won’t be finding any AS availability to YUL. That would be AA only.

AS starts putting out awards at T-330, but often they don’t publish good fares so the availability you will want may not show up until a couple of weeks later. There’s no guarantee that there will be additional seats made available once initial availability is gone.

Generally speaking Alaska award availability would be best on West Coast flights involving SFO/LAX-SEA in coach. You may occasionally find something going to the East Coast out of an Alaska hub. First class (what you would call domestic business on QF) is rarer and not common at all on transcontinental flights (and you would likely have a better experience on AA out of LAX/SFO to JFK).