I've been trying to get that sound for a while (the hard way, without having a P-bass strung with .110" LaBellas). I have the SansAmp VT Bass, and I am very pleased with it. It really helps me come close to the sound in those isolated Jamerson tracks, closer than I thought was possible using a Fender Jazz strung with lighter strings. However, the trick is to first get the instrument to put out a tone that's going in the right direction, which means the right strings, otherwise any pedal will hurt more than it will help.
I'm using GHS Precision stainless steel flatwounds on a MIM Jazz (stock except for Fralin pickups). I've tried several different flatwounds, and finally gave these a try, and I am glad I did, as these were finally a step in the right direction. The first couple notes I played with these strings gave me goosebumps, as that intangible "something" in the sound I was looking for was right there. Neck pickup volume full, bridge pickup volume set around 1/4 gives the best growl with my particular setup. Plucking the strings harder than normal is a big part to getting that "whomp" in Jamerson's attack.