Buying a new TT today

If you have Technics dealer make sure to check this turntable at some physical store, some people just don't understand what it is looking at the pictures online. You have to touch it, press start and stop button, put the needle of the record, adjust the tonearm ... and you will understand why this turntable is so good. Technics SL1200GR (in silver or black) is what you can buy quickly and easily. 

Ortofon M2 Red is an awful cartridge, it's entry level, forget about it. 

On Technics tonearm you could use many mid compliance MC or MM or MI, you can also use high-ish compliance cartridges (MM/MI) and if you will mount something like Victor X-1IIe you will be blown away, i'be been using this vintage MM on my Technics EPA-100 tonearm and it was shockingly good compared to many cartridges. Audio-Technica cartridges like AT-ML170 is amazing, actually many AT cartridges are great. I'm huge fan of Stanton and Pickering top of the line models like SC100WOS, XSV/4000, 5000, 7500.... stunning for Technics tonearm. Also Grace LEVEL II Ruby 

Turntable. You will recoup a lot more for your Debut Carbon than you might for your cartridge.

If the goal is to sell what you can get the most for, then maybe. I thought it was to get the most sound quality? I would hang onto the cart in order to have a virtually new cart to sell with the table. Most people at this price level are looking for a complete package. The table will be worth more as a complete package with the original cart. 

You will need to listen carefully as any potentially huge improvements on your Pro-Ject deck will be hard to find.

So, purely as a learning experience, does it really make sense to recommend upgrading a turntable, then immediately saying but it probably won't be worth it as any improvement will be hard to find?

IMO a TT is the way since the Project is an entry level and I doubt will show a big improvement with a new cart. With $2k to spend, I would set my sights on a VPI Scout. You may be able to find a used Scout for $14-1500 and have $$ left for a decent cartridge. The higher end Projects are good but not in the same league as VPI, IMO. Take your time & be patient.

One you may consider is the Clearaudio Ovation.

this one might be beyond your reach, but messing around in the price range you are in will likely eventually result in a similar net expenditure.

the Rega P10 ’package’ at $6000 retail will boost every piece of the current package you have to 2 or 3 levels above. and it’s a coherent, synergistic package.

https://www.stereophile.com/content/rega-planar-10-turntable-rb3000-tonearm-apheta-3-phono-cartridge

and if you can sell what you got, and get a 'deal' on this one......there you are.