IMO most of it comes from how he plays. I just saw them live last Wednesday (AMAZING show and great tickets

), and I had my eyes on his hands the whole time. His right hand technique is really something to behold, he reeeally digs in deep into those strings. Obviously fresh rounds, soloing the bridge pup and some OD will help very much in getting you there, but unless you really go at it with your fingers, I think it'll always be off the mark; the tone is in your hands, so to speak.
As others have pointed out before (this isn't the first time this is asked here

), Geddy Lee sounds like Geddy Lee on pretty much any bass. There are nuances in the tone, but be it his p-bass on their first album, his Rick in the late 70's or the Jazz aftewards, his tone remains quite similar throughout IMO. So before investing in a million different effects (which isn't a bad thing, mind you), put on some new strings and check out how he plays in live videos and try to emulate that.
ps.
When really digging in, I get damn close with my 4001
