I'm just wondering is there a "best" speed for an incident like this to happen? i.e the crew will have greater rudder authority at higher speed.
There is a speed at which the rudder authority is great enough to keep the a/c on the centerline in order to continue the take-off. It is called Vmcg. This speed will always be lower than V1 which is the speed at which the first stopping action must have been initiated in a Rejected Take-Off.V1 is often called a decision speed but the reality is the decision must have been made a fraction before V1 if the field is critical.
So here's the theory....if your engine falls off prior to V1, you reject which means you no longer have the assymetric thrust problem , if your engine falls off at or subsequent to V1 you are gauranteed to be above Vmcg and therefore have the rudder authority to continue the take-off.
Sometimes you have to increase your V1 in order for it to be above Vmcg.
Does that help?