scottfeldstein
Roots and fifths and a little extra.
You might want to investigate how you are attacking the string. What you are after CAN be achieved with technique! If I can do it you can do it! Unfortunately everybody's hands are different so how I do it may not "work" for you. What I do is hit the string in more of a downward thwack for instance like how Geddy Lee plays vs a more traditional plucking motion. Adds a whole new level of "grit" to the tone without touching a knob or buying anything new.
I think that's true to a certain extent. There's a lot of guys who set up their basses with pretty low action and have just this kind of right hand attack. The added fret/string noise really gives it some natural grittiness. I like it.
I don't think it entirely obviates the need for an OD pedal, but it's certainly another tool in the kit.