I'm not sure, but even if the two flow meters are calibrated slightly differently, wouldn't you get a consistent error? And wouldn't that consistent error/offset be washed out of the equation because you are manually setting an actual output volume that you measured in a marked shot glass that inherently 'accounted' for the offset?
I don't see how that gives you all the variation in your results from shot to shot, day to day.
When I have tried to measure volume directly, in a marked shot glass, I noticed that it is difficult to be consistent: do you choose the top of the crema, the boundary of the crema/liquid, etc. so you pick one of those as your standard approach only to see that from shot to shot and day to day and blend to blend that the ratio of liquid to crema varies. This is the reason many (most?) use weight as the metric for output rather than volume.
In any case, I agree with you that the volumetric measurement approach on the BDB does, for whatever reason, deliver an inconsistent result. It has been this way on two different machines for me. Since I have only seen 'recipes' provided in terms of dose weight and output weight, I didn't pursue the volumetric approach any further. It has been so long ago that I don't recall if I even got consistent volumes at all. I stopped using it and moved to weighing the output pretty quickly, so I don't know for certain how I determined to stop using it. It might have been because with crema variation I didn't see a clearly consistent result, or it might have been because I was weighing the shot and seeing inconsistencies. I'm pretty sure that I dumped the whole idea of fussing with the volumetric in one session, probably within a handful of shots from that session.
The subtraction of the three way valve amount seems pointless to me. The flow meter on the input side should be sufficient for the purpose: Since we don't dial in oz on the display for desired output, but simply press/release when we get the desired (visually measured) volume, the three way valve volume should not be needed for any calculation anyway. Whatever the flow was at when the shot was stopped should be consistent enough. The three way valve gets dirty, lifts some grinds off the puck which can affect the amount of water lifted off the puck, and the dosing itself can affect the amount of water on the puck to be lifted (and not all of it may be possible to remove via the three way valve). Volume on the input sensor at the moment the pump stops would probably be more consistent. The pressure can vary during the extraction, which can be affected by the grind/dose/tamp/blend which can also affect the pressure at the point of lifting liquid off the puck. Lots of potential variability there. If you have a dry puck vs a soupy puck, the volumetric subtraction will yield different numbers.
So perhaps it is not a calibration issue on the sensors (or not solely that), but a simple inconsistency in the amount of liquid pulled off thru the three way valve, which would make the fundamental approach inconsistent.
ETA: okay, I re-read your post: if the two flow measurements are in fact made across the OVP, then they don't take into account any variation in the flow at the three way solenoid at all, it is invisible to the calculation. So you could have a great deal of variation in what happens at the puck that will not be accounted for, and so that would explain the inconsistency, and I'd wager that this degree of inconsistency would be larger than it would if the measurements were made at the input side and the output side of the of the three way valve (though this would still be inconsistent).
I didn't see any specific reference to the flow meters in the video, but if the measurement is made only that far upstream, then I think that is why the volumetric approach can be so inconsistent. If everything else we do remains consistent shot to shot over time, including accurate grind changes to account for bean aging, the approach might work well enough to be reasonably consistent.
From my perspective, for this to really work, there would need to be a flow meter between the basket and the spouts in the portafilter