Could you express the idea in a nutshell?

Request that Parts 1-8 have the ability to automatically turn keyboard control OFF when selected. When the Part is not selected it acts as keyboard control=ON and participates in group of all Part(s) 1-8 that have keyboard control ON. But if this designated Part is selected then it will act as if Keyboard Control=OFF and will be selected as a solo instrument.

This would also work the same as pressing the "Keyboard Control" icon on the home screen of Parts 1-8 because what this does is both selects the Part and toggles Keyboard Control at the same time. However, request allows Montage users to use physical buttons rather than using touch screen.

Idea to add selected Part(s) to SCENE control would also provide a way to accomplish a similar result with slightly more flexibility at the "expense" of using (for Montage) one set of buttons - the SCENE buttons - instead of allowing to spread control over a 2nd set of 8 buttons.

The problem currently is that IF you want to "solo" a Part that previously had Keyboard Control=ON but want to turn that Part's Kbd Ctrl OFF in order to "solo" it - you cannot press a single physical button to do this. You have to touch say a scene button that toggles keyboard control then also press a Part selection button to solo that Part that previously had kbd control ON (now off).

Asside ...

A workaround if you have the Part space would be to replicate Part(s) you want to solo in Parts 1-8 with keyboard control = ON and copy these into Parts 9-16. Then just use the Part Select button to solo these Parts. Of course you'll also have to use a common level assignable knob to Part level assignable knob source->destination assignment at the common level and using Parts 9-16 like this may have you run out of destinations at the common level depending on the superknob usage.

I like your additional 3rd state idea posted on ideascale.