Lomcevak. So far as I can see the only difference between your version and mine is that I've assumed that Vr and V2 are either identical to, or functions of their minimum permitted values. I've made this assumption because it was certainly the case with most C, D and E category aircraft that I've certified where they've virtually always ended up chasing the minimum values since best available gradient and TODR is otherwise usually based upon lower airspeeds than the minimum permitted.
Not having flown or worked on them, I'm more than happy to accept that the climb performance / climbing acceleration performance of perf-A jets may push the best gradient speed during initial climb-out above the minimum permitted value of V2, resulting in a higher value than I was assuming.
In the meantime I agree that Keith Williams explanation is rather more elegant than my mucking about with equations.
G