Congratulations, you've discovered one of the "fun" nuances of migrating to AE. I used to provide shortcuts on the lockdown screen to SOTI scripts that would contain a kill_application script for this very purpose so that users could kill the app on their own. The last I checked, kill_application was not working in AE so that unfortunately is not an option. A good old fashioned reboot might be your only option for the time being. 

I know that you can directly link intents in the lockdown.

Maybe you can find an working intent that will exaclty do what you want ( in that case, to close the app) ?

Or you could try to find the intent that is triggered when doing a "force stop" in the app settings menu from android.

I know this is an older thread but I wanted to know if there has been any solutions discovered for this problem since the post?  I am in the same situation currently.

If you are in Android Enterprise with an A9 or higher device you can switch to Native mode in the lockdown instead of Activity Suppression and then you can actually re-enable the App Switcher/Recents button in order to re-enable the ability to kill applications natively from the device. 

We have Galaxy Tab A devices.  I have tried disabling the Activity Suppression but when doing that I lose the task bar and the "app switcher" button on the bottom of the screen.  Is there a way to enable them?  In addition none of the apps on the lockdown screen will open except the Mobicontrol app.

Just to note we are on an older version of Mobicontrol 14.2.

I think you would need to upgrade MC then. There are more native lockdown configuration options in the newer versions: