If there is anything that I've learned over the years, it's that perception is fucking everything. Period, end of story. If you can't get into a person's perception, then you're better off not trying. So the EU's best chance to screw with the various exit groups within the EU states is that it'll pull at least a mildly punitive Brexit and let the British's elected government's stupidity do the rest. This would allow the EU to have wiggle room in global diplomacy while allowing the EU to be seen as pulling the trigger. The problem with this is that if they are seen to be too punitive, it'll stain the EU's ability to do global diplomacy for a while depending on how bad it is both in perception and reality (and if it is Treaty of Versailles level? Oh boy would it look bad).