Dogma
How would you sum up V1, then? t is determined by consideration of other than the accelerate-stop criteria, otherwise you could have V1>vr.
I said Vmc because I couldn't be bothered typing "Vmcg or Vmca" as both matter. And, incidentally, 25.149(a) actually uses the terminology "Vmc" rather than "Vmca"; it is conventional to add the "a" for the in-air T/O config Vmc, but not necessarily 'official'.
And Vmu sets criteria which must be met for all takeoff speeds defined for an aircraft. Whether the field is balanced does not affect the need to respect the conditions set by Vmu (or any other conditions). As the takeoff speeds (V1,Vr,V2) are interrelated any single condition (Vmbe, Vmcg, Vmca, Vs, Vmu,..) may drive all the speeds.
Sonja
You might get a less adverserial response (and no less help, I think) if you asked this in Tech Log. But I don't see why you shouldn't ask here.