The issue of which electrical effect dominates is certainly up for discussion - only a set of analog simulations at various frequencies, pickup impedances, cap values and control settings will reveal all. Getting a reasonable coverage of the variable space would be a bit time-consuming. Are you aware of any papers on the subject? It sounds like something that one or more of the botique pickup vendors might have done. And, now that I think more on it, this is an obvious subject for an undergrad EE paper. Someone has certainly done this - more likely many someones.
And - sorry for any confusion - I'm indeed saying that I want the effect. I've come to rely on it to dial in on a good rhythm sound. I generally start with volume full-up and dial in a solo tone, then back down (sometimes way down, depending on how far into overdrive I was) until I get a more zingy rhythm sound. Sometimes it takes a couple of rounds to converge on something that works. It's just the way I've always done it. Again, maybe not for everyone.
Yeah. Sorry, I re-read your original post and it became clearer, so I deleted my post.
Helmuth Lemme has just released his excellent book in English, which I think is a must-read for anyone who's interested in guitar electronics and why different guitars and pickups sound the way they do. "Electric Guitar Sound Secrets and Technology". It was originally in German, so the translations are a bit dicey, but one can work out what he means.
Some of his work is here:
So I gather that as of right now, the JTVs keep their characteristic sounds as the volume control is changed (unfortunately, mine is in another country at the moment, and I haven't tested this).