Talked to PG tech support. The solution is to increase the velocity of the MIDI value being input to BIAB. There's two ways to do it, one is in BIAB:
Options->Preferences->MIDI Options->, and in the section labeled “MIDI thru” change the value labeled “Boost THRU velocity by” to 127

That comes close to resolving my problem: my keyboard now is on volume level ~60 while the backing instruments are set to ~45.

The other way to address the problem is to increase the velocity of the MIDI value being sent by the keyboard. I see no way to do that on my keyboard, and in fact there are many posts on the forums that say the Yamana P family of pianos don't output the full 127 value for MIDI velocity, which is consistent with what I see. The argument they make is to buy a real synth, like the Yamaha S90, if you want that kind of control over the MIDI values, or buy a little box called a MIDI velocity converter and hang that on the output of the keyboard.