Well, the most interesting things that have washed up are arguably Japanese ships which – disabled by the loss of mast and rudder – had drifted the width of the Pacific on the prevailing currents that you mention. Sometimes these were ghost ships, which sailed on after their crew were all dead of thirst and hunger, but in cases where the ship was carrying a cargo of food, some of the crew might actually survive this voyage and find themselves in the impossible, incredible position of being stranded in an utterly foreign place with no prospect of ever making it home.

We know most about this phenomenon from records made slightly later than the period you're asking about, during the Sakoku era, when the shogunate deliberately mandated that ships constructed in Japan were less seaworthy than they had been in earlier periods as part of the policy of (partially) "locking the country" – and hence were more likely to be dismasted or suffer rudder damage in a storm. But I also wrote on the possibility that castaway Japanese seamen had made it to Hawaii in the 13th century in an earlier response which you can read here. It's very unlikely these were the only examples of sea drifters dating to before the 1500s, and (as you'll read below), it's been seriously suggested that the number of Japanese ships that washed up in the Pacific North-West in the period to 1500 may have totalled thousands overall, and that these are plausible sources of the anomalous finds of worked iron artefacts that are sometimes made in the PNW, far from any naturally occuring source of iron.

To offer further detail, let's look at the situation as it existed in the post-1633 word in a response adapted here from an earlier essay of mine.