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Apart from "narrowing" P/A down to about 15 possibilities, I have got absolutely no handle on this. How do I start?!

21d gives thirteen possible E,L,T combinations, with E in the range 2-5.
Slot these 13 possibilities into 11a and just one combination gives a unique value for D and further restricts the range for A.

dylan - I think p/a can be narrowed further. 29d is a 2 digit square which has only 6 solutions.

Thanks, Crosswhit99. Using a quadratic equation from 21d, and my knowledge of Pythagorean Triples, I now have D,E,L,T.

Thanks also, Smartie, but in fact your idea was the first one I used. However, combining that with 27ac still gives numerous possibilities for P/A

I now have A, using the fact that D is divisible by A. That still leaves f options for P, and beyond that I'm stuck altogether

f = 4 ! sorry

dylan - how do you know that D is divisible by A?

From 12d and 20d - if I is divisible by A, and D+I is, then so is D

good call!

Grid A complete. But, after staring for ages, cannot see what to do to start to complete Grid B. Perhaps the last 4 digits in the first and last columns are significant? A hint re the theme or cipher would be helpful?