Most tube comps can be overdriven. The Orange Squeezer clones can be biased to grit a bit. Many other comps can be set to add just a smidge of dirt (or a click sound) at the attack of each note, by setting the attack control at one extreme or the other. The EBS tubesim is more about fatness and a very slight "furriness", not actual grit. I'm thinking a tube comp will be your best bet. Depending on your bass, technique, etc. you may need to put a booster pedal in front of the comp in order to OD the tube.