You’ve had Jason’s opinion. In my opinion, you don’t necessarily need a high gain phono stage unless you are fixated on a LOMC cartridge. There are some superb high output cartridges that will work fine with a good MM phono stage, although none of them are MC types, again, in my opinion. Stick with MM and MI type cartridges and you don’t need the high gain. For one example, Nagaoka MP500, which costs ca $900 and will drive an MM phono stage. It’s a Moving Iron type. If you do want a LOMC for well under $2000, then you ought consider Audio Technica, either the ART7 or 9 (both discontinued but maybe can be found NOS) or their new ART9Xi or Xa. Hana Umami Red (make sure it’s a Red) is said to be excellent but will cost more like your $2K upper limit.
I have owned many well regarded HOMC cartridges, and none of them was the equal of any of the above or of many other LOMC, MM, or MI types I own or have owned.