KTK,
(a) V1 is still restricted by VR which is restricted by V2 which is restricted by AFM scheduling limits
(b) if the takeoff is Vmcg-limited, reducing the weight generally will have no effect on Vmcg so the problem doesn't go away unless you increase V1
JimmyTAP,
While I don't have specific info re the machine, I suggest that
(a) Vmcg is independent of NWS so sideloads shouldn't come into it.
(b) the criterion is centreline divergence.
(c) at low weight, low fuel state the failure yaw rate may be such that pilot controlling inputs are inadequate to keep within the divergence limits .. hence the need for a higher Vmcg to improve lateral response to pilot control inputs. Flap setting may have some minor effect on yaw rate.