Thanks folks, typing that out gave me an idea I need to try. Maybe this is a hierarchical clustering problem followed by a linear programming problem to calculate the new node locations.
I think (🤞) that #MinimumSpanningTrees are the answer. Make a distance matrix of all nodes, then find the shortest path through all of them.
Oooh, this could be combined with raster analysis to calculate shortest weighted distance. Nit for this project, though.
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