I'm looking for a way to merge polygons across the empty space between them with a Voronoi-type result. There is a very similar question here, but the approaches outlined in the comments did not produce the result I wanted (it created too many extra polygons, and all were very jagged). So, I did it manually as you can see below. I'd like to know a way to do this non-manually as I have even more complicated polygons that need this treatment.
Edit: There's a buffering question here that may be useful to me so long as I clip the resulting buffer's world extent, but so far it has no answer. Also in my case whenever I try buffering this shapefile, the rectangular ocean boundaries wind up getting buffered as well.