My understanding based on discussion here in the forum is that the KSP will only pass through the MIDI channel of the currently selected track. So most likely you need to have the KSP in parallel to the BSP as opposed to relying on soft-thru and having them setup serially.
This is unfortunately, correct. There is no proper and full midi thru support, on the KSP. Midi implementation is pretty poor, to be honest. Synthcreep is correct and you can only transmit on channels assigned to the 4 tracks and nothing else. There is no way to have midi information sent to channels, outside of this, something I seriously learned the hard way, when I got my KSP, last summer. There is also other midi based limitations, such as midi CC, aftertouch and program change messages, are not passed through the unit.
I would SERIOUSLY raise this with support. Myself and many others have done the same and doing so, raises the chances higher, of this massive limitation being rectified, in a future update.