I may need a custom screw machined

[dtvmcdonald]

Also look at the nylon-tipped stainless steel set screws. They are
wonderful things, I used hundreds in my work holding in expensive
laser mirrors. I never chipped one!

[Dubis7]

Well, lucky me, the new screws worked.

Here's my now repaired Norelco Continental 300 next to my next project, a 1960s GE Toast R Oven

Thanks to everyone that helped me out!