My opinion is that you guys are probably wasting your time approaching this from a theoretical perspective. I expect there's waaaay too much going on for you to realistically model mathematically without using some kind of complex computer simulation. For example: All this node/ anti-node stuff only applies to standing waves. Traveling waves are also involved... my guess would be that they are largely behind the 'attack', as I can only imagine picking a string creating traveling waves, that will then decay into standing ones. Interference between standing waves, traveling waves, and multiple harmonics of each makes the situation a lot more complicated.
If anybody was ever going seriously try to figure this out, then I propose approaching it empirically:
1. Take a les paul, and a pickup with the flattest possible frequency response (to be really rigorous, work out its response to different frequencies and de-convolute with the data later)
2. Figure out a way to make the position of the pickup variable. Ideally while still attached to the body. (This would be easier if you were going to deconvolute the frequency response of the pickup with your data later, as then the pickup could be made smaller (there would in principle be no need for it to even resemble standard guitar pickup, as it's effect on the sound would be being removed from the data)
3. Connect the pickup to a computer to record the sound. (I don't know how good the analogue-to-digital converters in sound cards are, so if they suck then find a good one)
4. Play every fret on every string, and record.
5. Repeat 4 for a variety of pickup positions (and ideally for various guitars!)
6. Analyse the data. Fourier transform it, fit functions to the data and so on.
7. You now have functions describing frequency response vs pickup position and vs fret for a given pickup position for a given string, and what ever other relations you want between those variables.
This scheme should be able describe the effect of pickup position only. The overall sound of the guitar would be influenced by many other things also... (pickups, strings etc) .. and if you wanted insight into the overall effect you would need to investigate those too.
Basically I think you are wasting your time with over-simplified pictures of something very complex.
It's like all these alternative medicines that will chose one aspect of the very complicated system that is the human body, (eg enzymes, or free radicals or "friendly bacteria"), and then decide that everything revolves around them... when reality, while they may indeed be a very important part of the system, they are just a small part of a very large system.
While in principle what you are saying may indeed be correct, I doubt you will ever be looking at enough of the full picture to get anything useful from this approach.
Also, hello again everyone! (I haven't posted here in ages because I've been very busy trying to get a decent degree)... only one exam left now .