No pedals here.
When I got my Special 5H a month ago, I was thinking, gee, I wish it were a little more aggressive as you described.
I was mucking about setting up my new Special with my preferred strings and out of the blue, I decided to raise the pickup a bit to see what would happen.
Oh, man, now we're talking! Just that little bit of height raising gave the bass a lot more of that aggressive tone and I was missing a little at first. I measured that height change, but I can't recall what the measurement is, so when I get back home, I'll measure it again if you like.
Using D'addario Pro Steels helps the aggressiveness of the tone as well, I think. And I just prefer the Pro Steels over anything else.