Modifying Socket Head Cap Screws

[Toolmaker51]

Gee....over 2 years & still no answer to this question?��

K.........I'll step in.
Two nuts can work with issues.......so
Scattered here at HMT.net are 'lantern chucks', and best over all solution.
Next, with less initial labor.......
Coupling nuts [the long type] are better, just back the hex or socket up against a solid stop to not back out when cutter takes hold.
Or coupler nut in jaws with washer and lock nut in front. Good thing about nuts of course with hex bolts [HHCS] are same size, secure clamping and alignment. I keep handy at least two of any sizes I come across.
Socket Head Cap Screws [SHCS] the nut and washer work.
Or slip them in through back side of collet, in a collet block, chucked in jaws.
Doing a lot? Pick collet larger than screw head, make a headed bushing with screw diameter, saw cut one side open, partially on the other. When it breaks or flub the cutting, the head continues to orient as it was made. Plus it's a handle to retrieve from chuck or collet.
Or in mill, block in vise, just like above. Set a stop, dial in and go to town.