I went to a local industrial supply house and got a new bit for him to use in his measuring device.
And I dropped it off this morning. He didn't have time to measure it as he was doing production work, because one of his employee's was out sick, today.
He is planning on creating the socket in two halves and then inserting the two halves into a shell to hold it, and the shell will have the end for going into the boring machine chuck.
This sounds like it will work, because milling out the tapered slot in the two halves will have square corners for holding the bit end.

3. If the bit gets stuck then you maybe able to remove the two halves from the shell to release it.

4. the set screw presses onto the pyramid.

I found, yesterday, a lot of info about braces and manufacturers of braces but not a lot of info on the bits or what the angle was. Hopefully he'll be able to measure it and create a sample for me to test before we do a production run.

More info later when I have it...
But in the mean time if anyone know where to find the angle in a set of bit standards or how to find the bit standards; it would be great to know....

Thanks..

Jim Rogers