Thanks for the suggestions.
Regrettably holding by the shank isn’t possible because, assuming the 6 used ones I found at the bottom of one of my “keep after removal ‘cos they might be useful” box are typical, there is effectively no parallel shank. Tapered all the way up except for tiny land so the thread doesn’t hit the countersink.
Realistically they have to be screwed into something to ensure they stay concentric when being cut and to support the head. The overall diameter of a No 4 is, I believe, officially 7/64″ or near enough 2.4 mm in new money so the maximum core diameter is tiny. Probably somewhere between 5/64″ and 1/16″ say 1.9 to 1.6 mm in new money. Michael Gl would dig out the travelling microscope to look! If the head isn’t properly supported the screw will bend almost as soon as you look at it when working on the edge of the screw due to the considerable leverage.
Using aluminium rather than wood as a support material is tempting but I fear that anything soft enough to easily take the screw without damaging the slot will be a bear to turn. Certainly the only piece of relevant size I have is the horrible “2 seconds to a built up edge” stuff. There was a reason i was given 4 ft of it!
I like Jasons idea of shaving the countersink from the back. Have to be done by running down the taper rather than straight in. Probably in two or three steps so the head is supported. Straight in with an angled tool immediately destroys the support and the effective cut is large so odds are the head will twist off.
Face turning and deepening the slot with a slitting saw is an interesting idea. Major issue is going to be lining up the slot. It has to be dead nuts to look right. If I have an appropriate slitting saw I can set it up on the Bridgeport but it’s not really the right machine for the job. Much easier on a baby horizontal mill.
The right tool for reworking screw head slots is, of course, a slotting saw blade such as the long discontinued Starrett #249 set. Fit a short hacksaw frame. Square cut teeth with no set so you get a flat bottom and straight sides. High up on the “shoulda bought” tool list. But too young to understand when opportunity knocked.
On reflection I’ll try my Plan A first, Plan B will be cutting the back side of the countersink and Plan C will be trimming the face and recutting the slot.
Thanks very much for the ideas. So nice to have options.
Clive