The left side of the hammers is thinner than the right side, and the impact is stronger on the right side. (anyway when the hammers are located for a faster UC pedal, as it is the case often.
A less frank impact is more prone to create "simili" false beats, in my opinion. I did not notice that this could be something with the string.
If the false beat is real, it can be heard by plucking the wire.
The 1/3 -2/3 hammer location is creating some slight unbalance, I would investigate that first(I am not saying you are confusing things, just that I did not notice the effect you are talking about)
False beats can be hidden somehow, by changing the dwell timing while tuning, as you say creating a simile beat by working the stabilization time at the 2nd partial level so it match the false beat.
Due to incoherency in the partials spectra, (reasons may be the slight length difference noticed between left /right string, or other causes) there is always some room, when tuning an unison, if we focus on the fundamental energy that energy tend to straighten the higher partials, the whole tone moan slightly but this is not always very apparent (more at FFF). IF we focus on second partial or above then the fundamental is auto tuned, with more largeness)
But the moment where the partials are coupling may be soon enough before, the long term stabilization that happens (probably) via the bridge, and that is ruling the unison in his longer part.
That is how I perceive those things, whithout precise measure or analysis, but for sure the perfect coupling (reinforcing) of the partials is enlighting the fundamental if done soon enough in the tone. (I like to open the octave to help my ear and also to perceive the sympathetic resonance better) (sympathetic ???