"Balanced field length" seems to be the length of runway where there are no margins of safety over and above the accelerate-stop distance ...
I think that you are trying to make BFL into something more complex than it is .. viz., just a convenient procedure which makes the result of the AFM calculation, however performed ...
ASDR = TODR (TODR being whichever TOD case is most limiting)
no more, no less.
Its only real value is that it gives the quickest calculation and/or the simplest derivation of the speed schedule.