It is important to remember in all single engine asymmetric situations that the one thing that will always get you out of trouble and stabilise things, is to reduce throttle on the good engine.
Have a real engine out scenario and have to make a steep turn into the "dangerous" dead engine to make a field? Reduce throttle. Can't control heading? Reduce throttle. There's nothing that says you're not allowed to do that.
Sometimes in ME training stuff tends to get fixated on "full power on working engine" and it can lead to bad practice at times. I did numerous unstable and semi-scary approaches during my training because I got fixated on this. It's easily done.