Oops. Lathe workholding issues.

Then again. A Set or Grub Screw, at 1/4" ww is readily available here in Australia. Screw a nut on locktite the sucker.. Machine it to the diameter for head. Set screw Hex socket would be considerably smaller than a 5/16" screw Hex! Shoot you could even do a parallel knurl if you wants to.
Could slip a couple in the mail. pop.
 
Also, I did try the Torx bit. It is just a hair tighter. It is about .002 bigger across the flats than the hex bit. If all else fails, I might go for that, but it is still too wobbly for my tastes.
Then maybe just peen the end of the Torx bit a tad to get it snug in the screw head.
 
I should probably point out, as nobody else has yet, the existence of the Lantern Chuck. It's usually used for finishing a screw (e.g. after you've shortened it), but it should be suitable for re-threading if you don't mind a large groove at the top where the head is held.

I haven't made one yet, but it is high on my TODO list. For now I've got some 1/4" plate that I mount in the vise with drilled and tapped holes in it for the common thread sizes I encounter.
 
How about use a spot drill to put a small center in the bottom of the hex socket on the screw, then turn a matching point on the hex bit. should center it up and drive it.
 
Did you try Superglue, nail polish, or locktite, shoot even wood glue, PVA, shellac, dopping wax even bondo. Spit on the mother.
Nail polish, et al, would even allow you time to attain your concentricity.
Just need to know if you have tried it yet?

AAH! I step away for a few hours and I'm overwhelmed with ideas! Which is a great problem to have!

Okay, no, I have not tried any adhesives. I'm at a loss as to how that would help. It seems to me that due to the play between the hex bit and the socket I would just end up gluing it off-center. Unless I missed something. Which I might have.

I'm not sure to what you refer in post #31. Probably just my inexperience with this hobby, but I'm failing to see what a grub screw will do.
 
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How about use a spot drill to put a small center in the bottom of the hex socket on the screw, then turn a matching point on the hex bit. should center it up and drive it.

I'm thinking along these lines. I'm going to order some 3/16 hex stock here in the near future (like, next fifteen minutes) and I might do that with this, unless they fit just perfectly. I think the S2 tool bits I've got would be pretty difficult to turn down, but cold finished 12L14 or 303 stainless should be pretty easy.

I'm going to have to look at the lantern chuck sometime too. Not exactly sure how it works yet, but worth looking into.
 
other thing is, I have reread your OP, and note the thread @ 22tpi. Sure is a mongrel thread. Maybe, not available as a set screw!

edit. again, cut down a 5/16, cut your thread, and a nut..............yabba.....yabbba...............
 
Yeah, definitely mongrel! That's a good term for it.

I've got some hex stock coming from Online Metals that is supposed to be .1875. That's about .004 bigger across the flats than my tool bits measure, so hopefully that will work. If not, I'm going to turn a taper, glue it in, and drive it that way and see if that works. We will see when the stock gets here.

I sure picked a complicated project to learn all the basics!
 
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