Slingerlands and Ludwigs are the two American companies that sound the most alike, in my opinion. It's no wonder--they were built in the same way. Kits from the 50s will sound vastly different, though, if only because the Slingerland toms didn't have badges/vent holes, so there's no air escaping the shell. This affects the sound a lot, and the Slingerlands like this sound a bit more like Gretsch kits, in that respect.

I would look for the different interior from what your Slingerland kit has. Get one kit with a maple interior, and the other with a mahogany interior. They will sound different, for sure, in a subtle but noticeable way...

Or go with a 5 or 6 ply shell from the 70's. I believe both Ludwig and Slingerland used 3 ply shells with maple reinforcement hoops in the 50's/60's. If you want a different sound, try a 5 ply unimold Slingerland shell or the thick Ludwig shells from the 70's. Personally, I like the old 3 ply shells. You could always try the same shell construction or vintage, but in different sizes. That would give a little variety.