Are you using the monitor output EQ to further adjust the Kemper Kone, and that's what's causing the harsh sound in the Bose?
If so, does changing the cab in your profile make any difference? Since the Kone idea is to replace the Rig cabinet with an Imprint maybe using another cab that works well with the Bose would work, while leaving your Imprint for the Kone.
If still no good, can you use the Main outputs with their own EQ for the Bose? If you also had to send Main out to another PA, they should probably be OK with the same EQ.