Yes, "joystick mode" is complicate, as the mouse must use again the J column instead of K column for the directions. Also the principal Fire Button on "Joystick mode" has to be in J column to allow old games to read it. I think the best solution is, when in "joystick mode", to move the "Right Mouse Button" from L column to J column, leaving the "Left Mouse Button" on K column permanently. The original Boxsoft interface searches for the "Right Mouse Button" on L column, but no problem as it is "Mouse mode".
In "joystick mode" the "Joy1" port of the interface conflicts with the mouse port if you move a plugged Joystick at the same time. I think only disabling the common at Joy1 will work, but it's not a big problem if you leave quiet your hands...
Can it be done?