Vmca normally is determined for whatever turns out to be the critical case ... things like high side thrust engines, low altitude, etc.
As an aside, one of the oft forgotten aspects is that, as the GW reduces, V2 reduces (following the reducing Vs1) until the Vmca requirement becomes limiting (especially with a four engined aeroplane). As a result, one ought to be very careful to control roll during an early climb failure, lest the bank angle variation in Vmca present one with a period of excitement and a very real risk of losing the aeroplane.
Vr less than V2 ? ... could you be mixing the min V2 with the overspeed V2 numbers while at the same time just considering the overspeed case Vr ? If this is the case, and I can only speculate, V2, for the overspeed case, is scheduled above the min V2 value precisely for the reason that, at the (slightly) higher speed, climb performance materially improves. Perhaps you might expand on your initial comment ?