Re: Balanced/Inbalanced field length
Two different things are being confused here.
A "balanced field" is a runway which had the "stop" distance equal to the "go" distance. The stop distance is the runway length plus any paved stopway; the go distance is the runway length plus any clearway (inb essence a distance from the departure end of the runway guaranteed free of obstacles higher than the runway).
If the take-off mass is the maximum that the runway and weather conditions allow, then there is only one value of V1. If the mass is less, then a range of V1 speeds is possible, and for each type of aircraft there is a way of calculating that range of speeds.
So, you don't unbalance the runway by changing the speeds.