you tend to generate a strong roll in the same direction .. this is countered with deflection of the yoke toward the dead engine
Can't say that I've ever experienced that on the aircraft I've flown - noting that my experience is far less than many here. Would you like to expand in some more detail ? Perhaps you are considering the short term rolling moments while the initial failure is brought under control ? Indeed, for dynamic failures within a knot or two of Vmc for the current conditions one can expect things to be very dynamic for a few seconds while things are brought into order.
In short stop the yaw with rudder, bank slightly toward the applied rudder, and slowly replace some applied rudder with a careful return of the roll control somewhere toward centre
This appears to be the reverse of your thesis above ?
once achieved the minimum speed may actually be lower
There isn't any fat left in a Vmca certification exercise - generally the published figure is for 5 degrees favourable bank. Perhaps you might explain a bit further ?