The problems which I'm facing are too often very similar to what is described in this post by Hyder Hasnain: Mesh and shrinkwrap
Pasting together parts from different models, some of which contain complex shapes not obviously related to primitives. I've looked several times at the solidify, skin, and shrinkwrap modifiers and can't see how they can solve the problem.
Trying to use them on damaged meshes just asks them to assume too much. However, conceptually they might work if applied to small segments of the mesh rather than asking them to work on the entire object.
Can any of the three techniques (Shrinkwrap modifier, Convert to Convex Hull tool, Point Cloud Skinner addon) be used as a tool in edit mode on a section of the mesh? In other words, a sort of intermediate step between editing the vertices and edges and applying a modifier to the entire object?