Hey Adam,
I have no experience with photoelectric homing sensors as used on Elite Series. I propagate retrofitting inductive proximity sensors on the Original Series since the stock machines only have stall homing. The excellent accuracy and repeatability of inductive proximity sensors is known (one example are these ones) and was also confirmed here.
But, in practice, why would you re-home during machine uptime? Homing is only necessary once after startup.
What you would do is re-zero workpiece coordinates. That should always have a good repeatability. But you would only need to re-zero workpiece coordinates (with a touch probe or plate) if you moved your workpiece or fixed a new one.
By the way, if you just want to move the carriages to the home position, and you say it lacks some repeatability accuracy when you home with the limit sensors, I would avoid using it. What you can do is simply G53 G0 X0 Y0 Z0 in the MDI command entry field. G53 means “Move in machine coordinates”. This should not make problems with repeatability and accuracy, as you don’t rehome then. You may also program a target for G30 (“Go to predefined position”) and use this instead.