more about the bits and bobs?

Oh, okay. It sounds like the P values are not probabilities at all, but rather upper quartiles from the distribution. And this distribution itself is a function of the value of n.

Can you say what the 'bit and bobs' were that you did to the samples from the normal distribution? In principle, using (generalized) convolutions you should be able to translate those operations that you did on the samples into an analytical result that you would get with infinitely many samples.

Without knowing these details, you could use a phenomenological approach. There are various extrapolation strategies that might be useful. For instance, if you plot 1/n on the abscissa and 1/P on the ordinate, your data are roughly linear. Or, at least they're not so embarrassingly nonlinear that no one would try to fit a Michaelis-Menten model to find the asymptote. See Michaelis?Menten kinetics - Wikipedia, the free encyclopedia.