Hi, I also have a Mk2, but no hardware synths.
Assuming I’ve understood your issue, I think there may be some confusion over what Analog Lab mode of the Mk2 does. It doesn’t change the keys, just the assignment of the buttons, encoders & faders.
In the settings for Analog Lab (the VSTi), you’ll see an option for MIDI channel. By default it’s set to ALL. This of course means that whatever MIDI channel the controller is set to, Analog Lab will be heard.
So as a starter, I’d try setting this option to a single channel (different to your hardware synth) & see if that works.
Hope that helps.