It is largely a function of how picky you are going to be in the parts of the gun.
I'm of the opinion that the only AR15 you can buy from a Canadian vendor that is a proper 3gun build is a JP. But I'm pretty picky - love my lightweight barrels, aftermarket triggers, LW BCGs, minimal dwell time, adjustable gas blocks, 15" foreends, and a proper good comp. Guns like the Stag 3G get 25% of the way there at a price well within your budget. But to go full out 3gun race AR you are throwing away 80% of the parts on any off-the-shelf AR, so why bother buying a full gun. And the JP with all those features is something like $3500-4500, way more than I think it should be and way more than I would spend.
If it was me, I would be building from scratch. I was lucky this summer in that I posted a wanted ad in the EE for a 3gun rifle and of the two responses, one had those features and was well under your budget. So the third option is finding one used.
And the fourth option is to import. There's getting to be a bunch of decked out 3gun rifles in the States, and also a bunch of used guns that guys have put together with all those parts. Find one and import it through Irunguns.