Found the problem. Set Input Mode is EXTREMELY broken for mouse-controlled games unless it is set by an event by the current player controller:
My workaround was to remove the lines of code from the plugin that set input mode by reference and recompile. Then it all worked.
Theoretically it would be possible to set the plugin up to have the dialogue tree nodes call a user-defined event on the playercontroller, but that is beyond the scope of my project.