Why not the Stormy Monday bridge? It fits perfectly with the neck, is plenty snappy and rough around the edges.
In my experience, it's as bright as the Riff Raff, ie brighter than the Mule, but it's a sweeter bright, less "hard". Out of the three it seems the most versatile - it can get closer to Mule sounds than RR can, and closer to RR sounds than the Mule can.
I put off getting Stormies for years because I thought they'd be "soft" and not aggressive enough, even for me. I was SO wrong, I love my Mules and Riff Raffs, but my stock choice for humbuckers now is Stormy Monday.
I have an Explorer that has had the same issue you describe (overall muddiness). It's had my Riff Raffs - made for a kinda thin sound - and Mississippi Queens. They're in guitars where they work better now. I've wondered for ages whether I ought to be going hotter for the Explorer. I haven't tried Mules (mine are in a 335, and I don't want to take them out of there), but I think they could work. HOWEVER, at the moment it has the Gibson 57 Classics that I took out of one of the guitars I put Stormies in, I forget which now - and it's the best the Explorer has ever sounded for me... Now, I already know from an LP and an SG, that a guitar sounding good with 57 Classics will sound similar but better with Stormy Mondays. Mules are good too, they'll be hairier and rasp a bit more, though.
Bear in mind that it will depend on the guitar itself. I have two SGs, one with Riff Raffs, one with Stormies and, ummm... and they sound the same when plugged in and wound up!! They feel a lot different to play, but the sounds coming out of the amp are almost indistinguishable. The one with Stormies feels slightly more musical, but crank both and they both do the job you're after.
I definitely think you want one of the three - Stormy, Mule, or Riff Raff.
If "snappy" is the most important, then choose Riiff Raff.
If "rough around the edges" is most important, then choose Mule.
If it's a bit of both - I'd choose the Stormy Monday, and it has the added advantage of matching the Stormy neck (btw, when both are balanced nicely for height, the middle position on two Stormies is the most sublime I've heard so far).