I have not tried this, but having done a lot of implementation the "old school" way, I suspect that the s.linkTrackVars value (which determines which dimensions are sent on actions is still set), and therefore that is populating the default exit link.... however, I suspect that the two rules are triggering in parallel.
Question... with your custom link tracking the click, do you need the exit link to fire for the same click?
If not, here is a trick to disabling the default exit links for this click rule only....
Open your set variables action, then go to the bottom and open the custom code area.
Add:
s.trackExternalLinks = false;
Then, to ensure that other clicks on the page (just to be safe if the click is opening a new window tab, and leaving the current window open) will trigger the exit links, if they are clicked, add another action after your clear vars, use Core and Custom Code
Add:
s.trackExternalLinks = true;
Basically, for the duration of this action, you will be disabling the default exit linking, then turning it back on for the next potential "exit" click that doesn't trigger this rule.
If you DO need the default exit click, you can try this, but I don't know if it will work based on timing... but, add a custom code action between Send Beacons and Clear Vars, and add the following:
s.linkTrackVars = "";
Hopefully this will clear out the list of variables to send on your action before the default exit link tracking kicks in.....