The head brace you have there gives you opportunity (space) to enhance a simple lock. You could also locate it on the left side as it would have no connection to the depth stop.
You might be able to add some rotational adjustment to it so you can clamp the spindle near enough and then dial it in exactly using a pair of opposed screws pressing on the pin.
It strikes me that if you wanted two different angular positions of the spindle, a known number of degrees apart, you could connect the spindle to a zero’d rotary table, loosen the clamp, rotate the RT and reclamp.