I'm not sure what stage you're processing here. It looks like the blob-finding stage. The distance metric image shows where the ocean blobs would be (the high parts). Simplifying the coastlines is a good idea to avoid things like the big block around Hawaii that's caused by the little island breaking the topology. A good way to simplify the coastlines is to blur the basic land mask image and then convert the image back to two colors to get the mask back. Another useful simplification is to treat the land masses as including their continental shelves, because currents tend not to push up into the shallows of the ocean too much. The simpler you make your coastline parts before you calculate the distance image, the simpler your distance image will be and the less likely you'll have weird holes like Hawaii.

The blob-finding idea is to take the distance field, ideally from a simplified world image, put in latitude barriers (single pixel lines of land across the map) to separate the gyres, and only then calculate the distance field. You'll get nice blobs for oceans. The centers of the gyres will be approximately the high points of your ocean distance field. You can do the same sort of thing to get the continental highs and lows by season, but you'd need to calculate the heat equator as well, if I recall correctly.

It looks like you're using Hammer as your projection here, so there would need to be a barrier at the edge of the world as well as having the latitude cell barriers follow the curve. The laziest way I've found to avoid the edges and borders problems is to use a projection with a rectangular shape and flat parallels (Equirectangular works, but it has other undesirable properties) and repeat half of the world on each side, so that the world tiles seamlessly across the horizontal edges. The topology of the middle part will be pretty much correct, but nothing's going to be perfect.

All of that blob finding was to get a distance field that roughly approximates the major ocean gyres (and continental cells if you calculated those). If you look at the latitude of a point (to determine the cell #) and the direction of the distance field at the point, it will tell you if the nearby coast is the east or west coast (it also tells you the distance to the simplified coast, of course). This information can be used to calculate simple approximations for ocean temperature which feeds nicely into local continental biomes. You can also run a few particles downhill on the distance field over the ocean to pick up moisture and then keep going over land to drop moisture (they will get directed by the air currents around seasonal continental highs and lows). There are simple models that are just a lookup of average annual rainfall and temperature, and others that need to look at each season.