Upgrade entry level or start over?

I’d start with a cartridge upgrade, if you decide to upgrade your turntable down the road you can always transfer the cartridge to the new table. Good luck.

Having a look at your equipment I definitely recommend upgrading your Phonostage. You are using the Mani, right. The turntable and cartridge are pretty capable.

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I would say overall your system is fairly well balanced. Looks like you have done well so far at choosing compatible components at a specific level of performance. I think the weakest link is likely to be the Phonostage... it is amplifies the smallest signal and as such is really important. You would get a big improvement by getting a much better Phonostage. A better cartridge is not a bad idea, but then when you upgrade the turntable you may be limited buy turntables that go well with your cartridge. Besides, when you upgrade your turntable you can sell or trade yours as a working turntable and upgrade to a new table with a cartridge... this can be easier and cost effective. Also, I find fiddling with cartridges best done by a dealer. But that is me.
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Some thoughts on upgrading. I always shoot for upgrading to another plateau. To do this you need to upgrade each component very significantly... then slowly bring other components up. So, i wouldn’t do a shotgun approach (which you were not planning). Given where you are, invest the $1,000 in the Phonostage. I Rembrandt when I went from a $200 Phonostage to a $1,000+, it went from tinny flat to dynamic and punchy a whole new experience.

Do a lot of research. Read Stereophile and The Absolute sound and other professional high end audio magazines. A used Audio Research or other high end audiophile quality unit will be one you can keep for a long time. Then if you upgrade your turntable... you will be ready for it.

I would say start over. Imo at this price point the best turntable path is to buy high quality vintage. Vintage has gotten expensive but there are still good buys. Read some threads on lenco and idler drive turntables as well as vintage direct drive. Learn what models are just below the radar.
Oh and after a quick look at some audio sites, it will open up your options quite a bit if you were able to raise the budget to $1600 but with patience I think it can be done for $1k.