I would suggest going about the above from a different angle. Create a new user account and re-add processes one at a time, followed by extensive testing before adding another process.
Prior to that, though, a hardware issue could be the source of the problem. Using another keyboard is a better test than cleaning the current one.
With intermittent issues this can take very much time, even more than the procedure proposed above. And the point of doing the safe boot test as first measure is to see if third-party processes are involved at all. Otherwise you might search for things that don’t exist.
Sounds logical, but I would always make the safe boot test first. Then – if the issue persists – the keyboard would be the first thing to check.
The reason is: there can be hardware and software factors involved. For example my above mentioned mouse input issue had two software factors (BBEdit, Yoink) and one hardware factor (Apple mouse). If I had never made the safe boot test I would have blamed the poor Apple mouse for the rest of my time (since the problem did go away when using another mouse).
My suspicions would fall on the Logitech Control Center Daemon – try disabling that and see if problem still reproduces.
Note I said nothing about doing any of my suggested steps before your prior suggestion of doing a safe boot. That's why the part of your post I quoted was only the suggestions which came after you recommended a safe boot. I know there are users here who have third-party software which may install files to /Library (e.g., Karabiner), and I know that a safe boot eliminates such software as possible causes unlike the possible issues a new user account could reveal.
I do not have Text Expander installed and I am experiencing the same thing. In fact when I disable KM the problem goes away.
Did you try my suggestion of changing the hot key to "released"?
Yes I did. Still occurring. Where did you say to look for feedback on what KM is doing?
So you have the macro triggering after the Command-Q is released, and you’re still getting a “q” in the next application?
Well, beats the heck out of me. Something must be grabbing stuff off the event queue and putting it back on later - which is a terrible thing to do and always leads to bad behaviour.
Bingo! 
I've been wrong before about the cause, but early indicators are that the Logitech Control Center Daemon (LCC) is the cause of the mysterious "q".
I was concerned that my Logitech K750 keyboard and M570 Trackball might stop working properly. And, I did have one issue: The custom keycodes I had associated with my Trackball Back/Forward buttons quit working.
But KM to the Rescue!
The KM Macro where that I had triggered with these codes easily allowed me to add another trigger: "USB Receiver Button 4" and "... 5"
@Tom, my next step was to use Safe Mode boot.
So, for now, all is good. I still need to be observant for while longer to see if the "q" issue has gone away.
My undying gratitude to all of you that offered troubleshooting ideas. I think they all were good ideas. If removal of the LCC does not solve my problem, then I will definitely be using your suggestions.