If it were me, and maybe I know what type of tone you're looking for, I'd try to borrow or get my hands on a passive Fender Jazz bass with the normal JJ pickup design. Grab some fresh D'Addarrio strings, set the knobs to middle, then tweak to taste. Play through 10" speakers (if you can get an Eden or SWR cab 2x10 or 4x10), or even an Ampeg 4x10 and a tube Pre-amp, you should be able to get the source you want.
For DI you might also look for a SansAMP to give yourself a little more punch as well, everything set to 12:00.
For the plug-Ins you use, 8:1 compression at most, and maybe try the Waves Kramer Signature Bass plug-in. I also will at times use the A-type Console Emulation, although if you have Waves NLS, the Spike channel 29 is pretty punchy.
However, I recommend making changes on the bass side first. Deans are just fine, but a Fender Jazz in an SWR or Ampeg is going to resonate the way you may be alluding to. Don't overlook the SansAMP, though. For the money, this box is amazing! Best of luck!!