A workaround I found was to use "hot corners" to toggle the visibility of the virtual keyboard. Unfortunately this does require using the mouse, just moving it to a screen corner to activate a command.
You can access the hot corners tab from the accessibility keyboard settings (gear icon -> Preferences).
The "Hide/Show Home Panel" is the default and correct option. I like to unselect the "Panel follows Hide/Show Home Panel" so the Panel doesn't move around.
Note that this will only work if the accessibility keyboard is activated. This is definitely not ideal (a bit ironic too), but it's the least painful alternative I could find. Hope it helps!