I reckon if you could get there 10 years early you could probably prevent the entire thing. If you were capable of convincing some of the larger groups within the americas of the impending invasion, there were certainly people and resources enough to put together a small navy and start patrolling the eastern coast. Throw is some modern knowledge of firearms and metallurgy to help them develop some cannon, and Columbus never makes it to America.
Back in Europe people assume him lost at sea, and leave the atlantic untouched for another generation. With that much time to prepare, who knows how things play out.
I think it's time to start polluting the database with random DNA samples from discarded coffee cups amd random names from the electoral role. If we feed in enough junk then eventually they will hit on enough false positives to discredit the system.