I've had a couple guns, a Fox and an Ithaca field grade guns that had slightly loose actions. I fitted the hooks with steel shim stock from a pump company's machine shop. Cleaned the hooks and applied Loctite 609 or 638 retaining compounds. I only used 1 thousanths (0.001) shims. I worked without having to attend to the extractor for fit.

Just a touch of movement would probably indicate about a thou off the hook. Measuring the face, you might not even get that.

Question is, is it even worth getting the .001 gap tightened? I prefer spray welded fixes when possible.

I guess if you were shooting cases of shells you might wear the hook out on a loose action!