Great song, and great bass tone!
It's an overdriven low wattage tube amp with the treble rolled way down and the speaker farting out. Try using the neck pickup of your bass only, cranking your gain and playing with extreme EQ settings (high bass, low treble, mids to taste). Does your nemesis have a distortion circuit? Give that a try as well. It's not gonna sound identical, but you have a very flexible amp and you can probably sound close enough for the mix.
If that doesn't cut it, you could try various OD pedals or even some low-gain fuzz, but realistically, nothing's ever gonna sound like an overdriven low-wattage tube amp but an overdriven low-powered tube amp.