Actually, quick update. Try opening Adrenalin and going to Performance > Settings (the tab next to the tuning options, not the main Adrenalin settings). On the far right is a circular arrow RESET icon. Click that and it'll give you a popup warning about resetting all performance settings back to default. That seems to only apply to the settings tab you're in, not the tuning options. Make note of any customized settings you need to keep, then click OK. That looks to have unstuck the overlay and it now responds correctly, including the hotkey shortcut.
Still a bug that it was stuck at all, but hopefully this gets it worked around for you too.