Seems like there were a couple of things I skipped when making the explanation. My bad for not taking notes while I experimented. To fix your issues, first set Disable Player Controller Input (contained in ATBTT_PlayerController) to false at the far right of the Event Graph of the Game Mode (same place where I set Local Current Unit to empty). This should prevent input from being disabled after you have attacked:
Also in the the player controller in the End turn if the current unit is clicked comment box check the local current unit instead of the current pawn from the game mode. This prevents the issue where you click an inactive unit which is stored as the current unit and it skips straight to showing attack range:
Having a dummy unit could of course also work, of course. That basically comes down to preference.