I tried that - cloak and move then take a shot - which always works perfectly on most enemies. Like you said, Black Widow + armor piercing ammo = one clip and done for a Banshee. But it's like the Mirror Match opponents see right through it; even without taking a shot or firing a power after moving, they still make a beeline for me as though I'm not even shrouded.
Ehh, I guess I'll just keep working on it, try some different squaddies. Maybe turn the difficulty down to Normal. Thanks for the pointers!