I have achieved a similar sound to JJ. I use it at different time throughout a set of our original tunes and involves a TC Electonic NOVA System, but should be obtainable with a simple OD pedal as well as some EQ. Now keep in mind I wasn't trying to recreat JJs tone by any means I just found a tone I liked and stuck with it. I used to do it with a cheapo Ibane ToneLok OD pedal actually. I use the lowest amount of OD I can get away with on the pedal to get a nice gritty crunch and then I also have my EQ engaging some mids to help accentuate attack and cut through a bit. I usually find playing around with pretty much all frequencies between 100 and 2k until your get what you want. For me that's typically a slight rise. Around 180-200 and again around 1.5 to 2k and rolling off everything under 60 sort of like a high pass. That seems to work for this particular tone, of which I have several in a set, but most sounds are based around this slightly aggressive crunch. I should mention that this is the same setting I use on both my active PJ basses as well as passive Jazz and P bass, though it was originally set using the actives. I could enjoy a bit of retreating for the passive instruments, and one day I will, but for now it's working great. I know this is likely not what you wanted to hear, just spitballing. I have run through guitar rigs before looking for a nice tone that existed in my head, but never found it in a guitar rig. I have been experimenting with pedals and fx boards for years now and rely on them heavily for tone, although I don't use over the top effects. They do allow you freedom of expression with tone versatility though.