Dear MR,
I have a few questions/thoughts. Could get a thin screw driver in there and pry against the EZ out to loosen it? If there is any sort of gap, I have been able to dislodge EZ outs pretty readily because they tend not to have engaged very far. If it works, great then plan B, if not, plan B.
PlanB: What about just drilling the whole thing out and put in a helical coil threaded insert? e.g. a "Heli-coil"? If you are just holding a cover on, it should work just fine.
Plan C: new head. My time spent repairing a tractor tends to have a low price, but at some point...
This is why I find working on old machinery such a challenge- I go to tighten something trivial and then the next thing I know I am fifteen steps down some repair caused by the repair to the repair to the repair.
Good luck! I feel for you.
All the best,
Peter