Broken screw removal advice

There is a trick that can be done with two screwdrivers. Where one is held vertical and the other horizontal to hold the screw against the remaining side. This only works if the screw is not locked in (cross threaded or rusted.) Bit tricky in this place to use Alum, which is something I am learning myself. This will attack any iron surface and turn it to rust.
Most watches have the screws drilled through. There is a tool, which in theory can lock into each side of the broken screw. Using such tools has mixed results. It is easy to bung the plate as the screw is harder than the brass alloy in the plate. One can also drill out the screw, which can also cause damage should the drill wander as it will dig in between the screw and the plate.

You could try a tiny spot of oil under the screw head and under the tab.
Let it soak for a while and then use a fine screwdriver to push the tab in an anticlockwise direction (into the recess).
This should enable the movement to be freed from the case.