Thanks 
Again, fully aware that the issue I’m seeing may be entirely unrelated, and I’m planning to report it separately, but I wanted to leave my findings in case someone with a similar issue ends up as the symptoms can appear to be identical.
I noticed that my respawn functionality, which is handled in C++ by a derived game mode, spawns my C++ pawn and not my default blueprint pawn class as set in the editor. If I change my C++ game mode respawn functionality to use the DefaultPawnClass (set in the editor) then I consistently see the diverging pawns issue in a dedicated server environment. Certain materials also fail to render. Reverting respawn to spawn instances of the pure C++ class resolves the issues in a dedicated server environment.
This issue does not appear in PIE.