I have had a play around with the resonance and cutoff parameters on the BK9 piano tones. I hear no difference at all. The manual states that no noticeable difference will be heard by adjusting these parameters with certain tones as the default will be at the maximum.
Yeah, the filter suggestions were a bit of a red herring. As you noted yourself earlier, they don't work on SuperNATURAL sounds, but even on the other (traditionally sampled) piano sounds, pretty much any modern sampled piano sound will have multiple velocity layers. In the old days, a piano note might have only had a single sample, and the sound designer could use filter cutoff combined with velocity envelope adjustment to help give it some velocity-controlled dynamics, and then opening that filter (or altering the velocity responsiveness of the filter) could add some brightness to the less-than-high-velocity strikes, but these days, keyboards almost always use different samples for different velocity levels. So then you might be able to use a filter to reduce it from its originally recorded brightness, but you can't use it in the direction you'd want, it's not going to bring out brightness in the sample that wasn't there to begin with (or as you put it, it's effectively already at maximum). And resonance creates artificial peaks that are unlikely to be helpful here.
I'm putting the quality loss down to my amp, and the fact that I'm going from stereo to mono, but I have always done this. Besides, the styles sound quite good, as do some of the other instruments, like guitars and some of the strings and saxes. Just not the piano!
Piano is typically the hardest sound to get sounding good through an amp. It is pretty much the "go to" sound to determine how good an amp is. An amp with more coloration or weaker highs or lows won't be noticed as much on those other instruments as they are on piano. Also, for most sounds, you don't have to worry about stereo vs. mono phase issues because most sounds are mono (absent any effects).
Out of curiosity, I don't think it's been mentioned, what amp are you using?
I don't know why, but it seems that the cheaper keyboards have clearer pianos. Maybe it's just my ears and what I'm used to, I don't know.
I think sometimes "better" pianos can sound worse than lesser ones. One reason could be a difference in stereo-to-mono compatibility. I also have an "uncanny valley" theory here... that when a piano sound gets closer to real, its flaws through sub-standard amplification become more apparent.
Since you're okay with the sound at home, as you say, it may well be because of the amp and/or going from stereo to mono, even if other keyboards have been okay in that environment, and so that might be the perspective from which to address the issue, rather than adjustments to the keyboard or adding a second keyboard. But on the second board topic...
Someone has given me a Casio WK-3500 which I am going to try in conjunction with the BK9. Seems a strange combo but if I can just get a clear piano sound from the Casio, I'll be happy. Just a pity I have to lug an extra keyboard around with me to get a decent piano tone...I'm thinking of trying the Yamaha E-473 or the EW-425.
I didn't like the piano playability of the EW-425.I don't know how much of it was the particular piano sound, vs. how it played from that action. My Casio CT-S500 is pretty decent, though, if 61 keys is enough and you want something small/light and low-cost. Again, no 5-pin MIDI, so you won't be able to hardwire it directly with the BK9.
But getting back to sparing you from having to bring a second board... amp is one variable to address as mentioned... and we've mentioned stereo vs. mono, but not how to address it. Short of actually running in stereo, here's something else you can try. If you're using an output from your keyboard that sums the stereo to mono, try defeating that by just using an actual mono signal that is only one side of the stereo signal. So if you're using the L/Mono out of the BK9, try using the R output instead.
Though also, it sounded like your initial experiment with an iPad sound was reasonably successful, so maybe some more time spent on that could also spare you from having to bring a second board.