yet I want to have a good reliable ground connection.
Most modern BX has a bare wire runner just inside the armor and outside the paper wrapping covering the white and black wires. As I understand it
you're supposed to take this bare wire and bend it over the antishort you just stuck in so it doesn't fall out, and then wrap the bare wire back around the outside of the armor so it lays in the groove between adjacent wraps of the armor. Then fit the connector over that and clamp it so the litle indents in the clamp clamp that bare wire. That you're not supposed to have any of this bare BX wire inside junction boxes, unlike romex. The metal box is then your ground connection.
Some BX has aluminium armor sheathing, and it says not to use set screw connectors with it.
Why is it that there is no problem with this aluminium armor BX cable with copper wire inside, but aluminium romex wiring caused lots of trouble? The ground has to be able to take a fault current.