"What cartridge would you go to..."? That's a very good question. And the answers are very, very subjective.
Part of the answer is going to be driven by what you mentioned about setting up two SL1200's and potentially dabbling in DJ/Mixing. I'll be honest that I don't have any experience with the DJ side of things, but I would expect that the robustness of the cartridge is going to come into play. I would think that a rugged, low compliance cartridge might be needed to handle the back queuing and higher than normal duty? And maybe staying with a good MM design? (Guys, feel free to chime in if I am wrong or off base here...) If I'm right, then staying with the Ortofon 2M lineup would probably do well, with the 2M Black being the top of that line. A Denon DL-103 moving coil might also work.
Now, if you are trying to pull out all you can from the SL1200 TT, then I like a moving coil over a moving magnet. However, there are good choices in both MC and MM in the sub $1000 range. However, part of what may drive your decision is what the pre-amp supports (if it has a built in phono) and at what point you are reaching the "limit" of the SL1200. An Ortofon 2M Black is a decent MM. You also have choices from Hana (which get many positive reviews), Mofi, the Ortofon Quintet MC series (I've listened to the Quintet Black S and I liked a lot), and Sumiko. I seem to remember being told that the sub-$1000 Grado MC cartridges are not a good match for the SL1200, but I don't remember why.
Now, if you are going to go down the rabbit hole and go for more, then you have a bigger decision to make. The Technics SL1200's are solid, robust turntables with decent sonics. They have been the TT of choice for DJ's and commercial heavy users for a reason. But, you would probably start running into a point where the TT is starting to limit what you can get out of the cartridges at the $500 point????? (Guys, correct me if you think I'm off base here.) If you want to step up from there, you're probably would be looking into spending $800 to $1500 used (??) on a TT and $600 to $1000 on a cartridge to make it worth while over the SL1200.
In addition, you also start getting into the capabilities of the phono pre, especially the ones built into preamps. Then you start having to think about spending money on a separate phono-pre and interconnect cables. And that is a whole other subject. (Remember I said "going down the rabbit hole"? Don't you just love this hobby. LOL)
So, as I was typing this, I started to think about what I would do in your position... You seem to have your heart set on the Levinson pre and 532H amp. I don't think anyone would fault you there. So, get those two pieces, hook them up with your existing CD, tape deck and TT and get used to their sound. (It is going to sound much, much different than your existing Adcom setup.) You might find that you need to upgrade the cabling. While cabling DOES MATTER, but you don't need to go off the deep end and spend crazy money either. (You never specified what cabling you currently have.) At that point, then I would look at your cartridge. Drop $700 to $1000 on a cartridge and live with it for a while. If you are happy, then excellent. If you find things lacking, then upgrading the TT or adding a separate phono pre would be the next steps.
As I said before, the key is, take your time. Don't rush things. Do your research and ask questions. And Enjoy the Music.
Hope this helps.
Jeff