I suspect it would have to do with the presets for the Main Campaign character creation, or whatever is used to randomize the player characters prior to adding them to the screen. All of the times I removed Player2 from the process, Player1 would be inserted into the 2nd character position (right side of the screen) and wouldn't be customizable.

In any case, my brief testing up through meeting Zixzax and obtaining the Teleporter Pyramids showed nothing out of place, so I'll leave my solution be for now. If it really becomes necessary I could just remove all of the Player2 references, but I don't think it needs to come to that.

Here's a link to the first version of this mod, if anyone wants to take a look.
Journey of the Lone Wolf (EE) early test version