Agreed, the motivation to move to the "1-g" stall speed definition was to avoid the variability and nonsense that was inherent in the "min speed" Vs methodology. Whereby a skilled TP could always shade the manoeuvre to generate a speed that was, shall we say, on the low side.
BUT, Vsmin and the 1.2Vs rule "worked". V2 wasn't causing any safety problems. So there's no way industry would have accepted simply changing Vs to Vsr and bumping up all the speeds - because Vsr is ALWAYS higher then Vsmin, since 'g' is less than 1.0 in a Vsmin stall. So, they went with equivalent safety - and picked a V2/Vsr ratio which on average would give an equivalently safe V2 speed. Basically, the same aircraft tested "both ways" would on average give a Vsr about 6% higher than Vsmin. So, knock about 6% off 1.2 and you get 1.13, hence the 1.13 Vsr ratio.
That, however, is an average. There will be specific aircraft where it works the other way, inevitably. One example would be an aircraft where the stall is completely defined by stick pusher activation. In such a case the slowdown to the stall will be pretty much at 1.0'g' - there's no aerodynamic pre-stall buffet which might be associated with a slight drop in 'g' to 0.98 or so. As soon as the pusher fires, the pilot's going to recover. That is pretty much going to be Vsmin right there. It's also going to be the Vs1g speed as well. If nothing else applied then you'd have Vs1g=Vsr=Vsmin=Vs. Which would put the Vsr-derived V2 some 6% lower than the Vs-derived one.
To account for that, at least some Vsr/Vs1g aircraft with pusher-defined stalls apply a 2% penalty to the Vs1g to derive Vsr. That still gives a 4% margin, where the Vsr-derived V2 can be lower.