Is the time required to repeatedly home going to add a significant amount to the total "print" time?
If not I think you should simply accept having to home to the existing endstop.
The problem with an endstop in the middle is that the starting position for homing could be to either side of the endstop. How can you determine which direction to move?
One possible solution would be to implement a closed loop control system where the actual position is always known.
Frederick