Reviving an old thread to add info.
I have a Parker 955 (5" jaw, fixed base). I used a hex key set screw (all I could find locally). It's a little too long, but it works. The set screw I used was a 7/16-14 x 1/2" (shortest available). Instead of a cut piece of rod for the friction shoe, I used a 5/16" ball bearing in the hole. The spring was a #88 Select-A-Spring with 1 1/4 turns cut off, although 1 1/8 turns would have been better.
When I get around to cleaning up the vise, I may cut the set screw down so it's flush, or replace it if I can find a slotted set screw in the size I need.