Losses. They try to maintain a certain level of navy strength. Make sure every ship is sunk as soon as they leave port, in this way AIs get to build more ships and you get to sink more.
You can also send some corsairs to Asia(Indian Ocean and Pacific Ocean), there should be a lot of (Mughal/indie, Indonesian, Japanese) triremes to sink.
You also get to sink quite a few ships before wiping out the Portuguese.
I get to finish in 1480 because prerequisite techs for corsairs are Gunpowder and Optics, which becomes available rather early. If it were Astronomy, I can imaging the winning date being 15~20 turns later, during the late 16th century. Meanwhile, not in every game can you get Optics from Arabia, so I consider this game to be a bit lucky.