The solution is to map the Command Option Q FOR SCREENCONNECT only. Not for the apps that you will be controlling on the remote computer. I don't give a fig if I have to use a special key sequence to quit Screen Connect. As long as when I quit a remote app I don't kick myself out of Screen Connect. The keyboard mapping solution works GREAT for me.
I find that most Command and Option shortcuts do not work properly on the remote client.
Command Q quits the screen connect session - not the app running on the remote client.
Command Shift Q starts a log out of your own computer - not the remote client.
Sometimes Command Shift A opens the Application folder on the remote computer - sometimes not.
Sometimes Command Delete moves a file to the trash of the remote computer - sometimes not.
Customer support service by UserEcho