Integrated with Phono Stage under $10K

The Accuphase E450 can be fitted with an internal phono card and its not bad at all.
The LFD Zero LE III can be ordered w/ built in phono stage and its good as well.
But I think the external ones will somewhat have an advantage over the internal built in ones though.

I have a Vac Avatar Super and it is very good and the phono is a pretty decent MM. As suggested above, you can do better with an outboard phono that is in line with your cartridge choices. At your budget, I think that the new Boulder integrated is within reach (but haven't heard it) and it doesn't have a phono.

What about the Classe CAP-2100 Integrated? List price is $6,000. I believe a factory installed phono preamp dual mono moving magnet and moving coil for turntables (a $500 upgrade) is also available (please confirm this option). I own the Ayre AX-7e Integrated amp and like it very much. Simaudio also makes several integrated amps in your price range.

I found the Classe a little bland, especially for the price. No comments on phono, since I didn't hear it.

The older Sim i-7 sounded a lot like the Pass INT-150 to me, with perhaps a little less mid-bass emphasis. Very clean, very fast, and very neutral. I haven't heard the new series of 600i or 700i--Sim is sure getting up there in price at the top end, but they have a number of amps (maybe too many?) so you can't fault them I guess?

If vinyl is your main source you're going to want an outboard stage, especially at the 10K or below price arena. I mean, just as an example, you could get a Luxman 550A II and any number of good phono stages (nagra? Einstein? etc) at list and still be in budget.

I went from a stingray to an audio note soro. there is a model with a phono stage but i did not need it so cannot speak to that. overall the soro was quite and improvement on the stingray, particularly with the right tubes.

good luck