However, I found one piece of software that helped - Voice Meeter was able to pick KA6 and route it to another virtual bus, which in my case is Realtek Audio output. Only from there I was able to record what I needed.
So, at the end of the day the mixer was only necessary to mute mic playback. I'm also now able to mute monitors with one button, so there's a chance I'll use them more often.
Finished all this at 11 PM and have no more will to record anything today