bridge volume off, neck at 100%, tone all the way up. bright strings and a high mid boost. lows to taste. single coil grind with good low end 
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Backing off the neck pickup a little bit does add more midrange, something I need right now.
Interesting, cut 800 Hz? I was recommended in another thread (http://www.talkbass.com/forum/showthread.php?t=518734) to boost that area for clarity.
Paul's tone in those clips is exactly what I want.
all knobs maxed. flat on my amp. i use flats on my bass so it's pretty tight on the low end and soft on the highs.
There's not a lot of upper mids in Paul's tone on those clips. It's all about just slightly backing off that neck pickup and playing with a good, solid attack pretty close to the bridge. Amp settings are difficult to talk about, since every amp, every room, and every amp/bass combination has its own inherent voice.
However, I believe my Sadowsky single coils are based on the Antiguity II's (I think), and there is a LOT of upper mid presence. So, I back of just a touch of upper mids (both my TecAmp and Markbass heads have the upper mid control in the prefect place... the designers must be bass players!).
Most of that tone is again about clean, strong right hand execution reasonably close to the bridge IMO.
I have some clips up somewhere of my Alleva's through my TecAmp rig. The TecAmp rig is flat with just a slight cut at 800 hz, and there is part of the clip that has the neck pickup rolled back a touch, and the passive tone control back a bit with me playing over the bridge pickup. If you listen to that clip, you will hear what I'm talking about (it may or may not be the tone that you are looking for).
I'll PM you the clip.
K