Thank you for looking into Steinway's technology in more detail. However, there are a couple of things that don't quite feel right about it.
Firstly, even if the sensing delay could be reduced to a couple of milliseconds, which I believe is perfectly plausible, I doubt whether the velocity of traditional solenoids could be controlled with enough accuracy to replicate the velocity exactly. They are on/off devices, so the only way to moderate the velocity is by rapidly changing the voltage by extremely small amounts. This I am supposing must need a feedback loop with a very complex function to account for different types of mechanical friction, electromagnetic impedance along the solenoid's coil and other factors that associate the voltage with the instantaneous velocity.
Alternatively, one could use a stepper-motor style linear actuator, which would certainly be very precise and could theoretically be powerful and fast enough to emulate a traditional piano's hammer. However, I have never seen such specialised stepper motors advertised, nor one small enough to fit in an unmodified grand piano action.
All in all, I don't believe that Steinway's really do have that capability, and I suspect that, whatever their measuring accuracy is, the precision of the actuator itself is more like a crude correlation to a few dozen levels of force than the claimed hundreds of levels. Of course, they do have a very slick-looking player piano, and I suspect that it what really matters for their clientèle.
On to your second point, I'm pretty sure that 4ms would indeed not be detectable. By 10ms I think I would be able to hear it; maybe there are people who could hear a delay shorter than that. As for phase, you can definitely detect the relative phase of two identical tones, but since an acoustic piano has up to three different strings each with complex harmonics I'm not sure you could pick out the phase of any individual tone that easily. However, I will admit that I am tempted to try now! :)