It ought to be possible to determine which of 25.107(e)(1)(iii) or 25.107(e)(3) is determining Vr by looking at V2.
If the V2 is constant, then I'd be pretty much certain that speed spread is driving Vr, since a constant V2 would imply that one of the V2 requirements is dominating, and that Vr is being determined based on V2, which would point the finger at (e)(1)(iii).
If the V2 is non-constant, then I'd be a bit more suspicious that it might be something else, but I'd still be more inclined to look for one of the V2-drivers, not (e)(3). The Vr-5 requirement is also an OEI case, so the thrust/weight isn't varying between the Vr and Vr-5 cases for (e)(3) at a specific altitude; I'd therefore expect that if the Vr-5 case is driving the choice of Vr that it would be doing so independent of thrust (and hence altitude).
I'd have thought the Vrmin requirement (e)(1)(iv) would be more likely to drive Vr than trying to balance the Vr and Vr-5 cases, though. For the Vr-5 case to be important you'd have to be rotating at a pretty low speed, so that either:
(1)the increased alpha at lift-off is pushing up the drag relative to the Vr case and seriously degrading the in-air portion of the takeoff (since the ground run is about 10% short to start with, the in-air portion has to take quite a hit); or
(2) you aren't actually achieving Vlof any earlier, and the aircraft ends up doing something close to the cert Vmu test - but that would only be the case is Vr is really close to Vmu, hence my comment about (e)(1)(iv)