Even if you could do it, leaving a paper trail about your trip to HAV wouldn't be too smart.
There are folks on this board who have visited HAV illegally. Search for their posts and learn a ton.
From what I can tell, flying on a CO award ticket to Cancun and then paying $200 US Cash for a r/t to HAV might be your best bet. Other potential "jump off" points include NAS or YYZ.