As the main question asked is if there is a way to automatically blow off into oblivion queries running over n minutes:

I have to agree that is not the way to go about it. I am not a fan of a wall of shame either for it delivers a message on how you want to react to adverse situations. This is not something I would highlight on my resume for what I see so far is a lack of effective communication. This needs to be brought up to your client (whome you of course report to ) and make them aware of the costs involved ASAP. Then a meeting should probably be held where you explain how you managed to optimise badly written code (though I wouldn't use those words) and how to have more fast coordinated stuff going forward. We all learn as we go along.