Well since I'm up to my neck in FV-1 I'd like to leverage the capabilities of that thing to try to accomplish some of these goals. So, for example, while it does have a 2-instruction all-pass, and if you set them all to be the exact same length, you can "tune" where the pwip occurs, even if I devote the entire 128 instructions to this, minus necessary I/O, it still does not get into the zone I am looking for. Mind you I am looking for Pwipzilla here. So to answer your question more directly, yes I'm looking for an analytical way to describe it and there is another paper by Julian Parker that goes a long way towards that. It' just that even his samples, while showing some evidence of pwipiness, is still more subtle than I would like.
I do recall a Johnson J-Station amp modeler which I had years ago, and actually liked patch 22 on it pretty well (you know the one). It had a spring emulation which sounded an awful lot like a sampled pwip that was level triggered. This is NOT what I'm after!
I've started doing some spectral measurements of recordings as well as my own reverb algorithms, and if I didn't actually have to do something else in order to pay the bills, I'd probably be a bit further down the line on the whole process.

Here's another paper that is focusing in on what I'm after.
http://dafx09.como.polimi.it/proceedings/papers/paper_36.pdf