I think you will find that the screws on a Parker Hale RALS, RANS, RAHS rings are likely #4 or #5 BA threads - that is a British thread system, not used much here in North America. If you take one out and measure carefully with a caliper, you can likely find what it is on the Internet. That BA series is used on some British made automobiles, through, and I did find some #4BA screws from a British auto parts supplier. I could only imagine that you could get those taps from Britain - I have bought several times from Tracy Tools, but you better really want and need them because its a long way across that ocean.
Edit - just dug through my drawer of goodies - I found one Parker Hale RAH3 ring with slotted screws. I removed one and checked and it is indeed a #4BA thread. Has a thick flat bottomed head. All the rest of the Parker Hale rings I have are with allen head screws, not slotted ones, and they too are the #4BA thread.