The OP pointed out that unfortunately, the mechanical LPF does not work in video mode on the K-3.
Going from around 24 MP to 2.1 MP involves some pretty significant line skipping, so I don't think that you would see any difference when comparing a traditional LPF to a sensor with no LPF. Maybe it would be possible to kick up the K-3's mechanical LPF, but you fundamentally have the same (i.e., low) pixel density, so I have doubts that would help.
Sensors are getting better all the time. One of these days it will be common to read and process all the pixels on an APSC sensor, not quite there yet though.