Not sure where you got these numbers from, but I did a bit more digging and found this Mi-24D flight manual from the very awesome Cold War Air Museum (CWAM), link here: https://mudspikefiles.s3.dualstack.us-east-1.amazonaws.com/original/3X/7/a/7ab064a7f951b9f0325354f257f5e58c571936d6.pdf. According to this manual, the airspeed limit for sidewards and backwards flight is 10KIAS, which is very close to your numbers. I've also seen some manuals translated from Russian that state 10m/s, but I'll leave that discrepancy aside for this discussion.
So to check out the tail rotor VRS theory I went back into DCS and repeated the test with no weapons and at 50% fuel (so that pedal authority would be less of an issue). I repeated the test but accelerated from hover into lateral flight to the right much more gradually. Referencing the hover speed indicator, at speeds below ~18KPH the Hind weathervanes to the right, requiring left pedal (or rather a reduction in right pedal) to maintain heading, indicating positive directional stability. Once ~18KPH is exceeded, the yaw tendency rapidly reverses, requiring an accordingly rapid right pedal input. Maintaining this flight condition resulted in a yaw oscillation, requiring alternating left and right pedal inputs to maintain heading control.
This behaviour is consistent with tail rotor alternately entering and exiting VRS as the heading oscillated, with the according pedal workload. I'm really impressed that this aerodynamic phenomenon is being modelled in DCS!
Case closed I think.