Gonna be honest here, I don't like how the area build commands were implemented for antinukes / anchors / umbrellas. Here are 3 different sphere tessellations: Top one is a cube map, which is what PA currently uses for its planets. Bottom left is a UV sphere, which is what the area build commands use. Bottom right is an icosphere, which has relatively evenly spaced vertices. For area build commands (and honestly, most other things too), a UV sphere is the worst of the 3 options. The vertices are not very evenly spaced at all. The cube map has some distortion as well, though not nearly as bad as a UV sphere. I think it could work fairly well. An icosphere is about as good as you can get for a uniform spherical surface. There's very little distortion. Only problem is that, as far as I can tell, there are large discrete steps between levels of detail in an icosphere, so you wouldn't have much control over spacing. Cube map may be the way to go because of this. EDIT: Actually, scratch the part about needing large discrete steps between levels of detail for an icosphere. For some reason I was thinking you had to divide the triangles iteratively, which isn't the case. You can get pretty good intermediate levels of detail, so I'm going to go back to suggesting an icosphere over a cube map.
No mods at all. I love my vanilla. It happens with Umbrellas too. You get clusters of them in almost the exact same spot clipping into each other. Rainbow icecream master race.
The death star planet would make the icosphere build pattern really awkward for things built on the ground.
The trenches might mess with it a bit, but other than that I don't see how it could be any worse than a UV sphere or cube mapping.