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ortolan, do you mean deciding which of the 4 grid orientations is correct once you have all 4 values ? If so, first establish where s and t must go (the third cell of 7a is governed by the fact that 16d cannot be 591), then 14d and 22a restrict the options for placing p and n.

I'm going to have another crack at this tonight....thought I was doing ok but like ortolan @ post 29, I got stuck with finding n and p to fit with my s and t.
if you are still around crosswhit can you clarify the second sentence in post 31? That would help me! My s and t are two of the lowest 9 digit roman primes - is that right? Including the very lowest.
Also did we establish that 2 (ie II) is not a two digit roman prime? I think actually it is, but am going with the other two options for the puzzle.....

2 is a prime but it doesn’t fit with the equation as s and t must both be odd.

Oh yes we'd never make the equation balance with only one even number available. So that sorts a and b.
Have I got my s and t right?

Yes, assuming you have them the right way round!

I was sure I had, following the advice at post 19, - that the third cell of 20a cannot be C. Which I thought I saw the logic of, but now don't, if I'm honest.

Sorry I mean post #12 not 19.

Not sure I follow that logic either and I don’t have the grid in front of me but you can fill in 7 of the digits in both s and t anyway as they’re the same in each

If I remember correctly, I looked at the fourth cell of the upper 9-letter entry, and saw it couldn't be X, so must be L. The second cell of the 6-letter entry below it is X, regardless of which one it is.

Thanks for that, agree about the X under the L in 7a. But I'm back where I was yesterday. As I have the second letter of the other 6 digit number as L. So I end up with two LLs in the middle of 16d, and there's no such number.
I do have a pair of numbers that work for the n/p equation so maybe there's another pair of 6s that also work.