It is unlikely that more sail would bring the boat up to greater than wave speed, which may well be of the order of 10 knots, indeed it would be unwise to try to achieve that, given the chance of hitting the next wave at an angle and turning side on. As for the idea of taking the waves at an angle that in my view would be a bad idea as it would immediately swing the stern making a broach more likely.
It is difficult to avoid motion like this in such following seas and once a yaw starts it is virtually impossible to control. The key seems to be deft steering at the crest to have the boat square. The forard sail, possibly a staysail or storm
jib trimmed on the centreline and a simple drogue can all help in this.