Ah, gotcha. It sounds like the K-MIx is working as a post-fade send (as effects tend to be, because in many contexts, you want the reverberated/effected component to fade away as a channel volume goes down).
But - perhaps you could also set it up as a pre-fade send? The channel volume then wouldn't affect the amount being sent to the aux channel. That looks like it's configurable on the K-Mix:
The aux sends for input channels 1–8 can each be set to function as a pre-fader send or a post-fader send. The channel select buttons are used for changing and displaying their current state.
- Press and hold a channel select button for 1 second to toggle between pre and post; the channel
select button’s LED will change color when successfully toggled.
- Green LED = Post-fader
- Red LED = Pre-fader
By default all aux sends will be set to post-fader.
So if you swapped your channels to pre-fade send, you'd then be able to turn the aux signal all the way up, and the dry signal down, and you'd get 100% wet sound out of the channel the BAM is on (7/8 in my example). But - you'd also be able to have wet/dry signal together on other channels, or, indeed, entirely dry channels around them, if you wanted.
It's not as easy as having actual channel inserts, but does that get you any closer to what you'd like?