I think you should address four items. I would look at an integrated amp, a new turntable, a new DAC and a new phono stage. You could spend a lot on any one part so it is a balancing act but the good news is you have lots of choice. I am going to make a few suggestions for each component but realize there are many options beyond this.

Integrated Amp - Peachtree Nova 220SE for $1999. It has a great internal DAC and is an awesome and powerful integrated that is actually in the same league as your Pioneer for power with 220w. NAD C375 BEE is a great unit, 150w and a monstrous transformer. It does not have an internal DAC and is $1499. Both are super detailed and a touch warm.

Turntable - Rega RP6 with an Exact2 - gorgeous, ultra detailed table with pace, rhythm and timing that Rega is know for with ultra crisp bass. $1999. Clearaudio Concept with a MM cartridge. Ultra precise and completely un-colored sound. $1600 plus a dust cover which I think will be $220. Another great choice would be a Music Hall 7.1 $1295 with an Ortofon 2M Black $795 or a Dynavector 10X5 for $550. The Music Hall is smooth and neutral. The 2M Blac is a great cartridge, as is the Dynavector. They will each sound a little different. I love Rega personally, but a listen to a lot of jazz and classical and their cartridges are amazing for that genre. If I listened to hip hop, I would go with one of the other two.

Phono-stage - Musical Fidelity M1 - LPS or the Vincent Audio PHO - 700. The MF is $450 while the Vincent Audio is $499. Both are exceptional and would work wonderfully with the Peachtree or the NAD.

With the NAD, you are going to need an external DAC. I like the Peachtree DAC iTx. It uses the ESS Sabre32 chip in a superb implementation. At $299 it is a steal. You could also consider the Musical Fidelity V90 DAC for $299 which seems like a universally beloved device. Either would work wonderfully with the NAD

You will also need 2 - 3 cables depending on your device choices. Audioquest Golden Gate is an outstanding cable for the money and you will pay $100-$150 for 2-3 cables.

The most expensive options, Peachtree Nova, Music Hall 7.1 with Ortofon 2M Black and a Vincent Pho-700 with cables would total about $4750. The least expensive, NAD Integrated, Peachtree DAC iTx, Musical Fidelity M1-LPS and Clearaudio Concept MM with dustcover and cables would be about $4220. Any combination would be freakin' amazing IMO.

I think you will be surprised at how much a turntable upgrade will make a difference. It is not the age of the Debut Carbon - you would be buying a better motor, tonearm, cartridge, etc... And that all adds up to improved sound. Your system is only as strong as the weakest link and that Debut Carbon, although a wonderful entry level turntable, would remain the weakest link.

That Prima-Luna is a sweet integrated but a big step down in power output from your Pioneer. If you listen at high volumes or have a big room, you may find it underwhelming. I read the Stereophile review of your speakers and it sounds like there is a trade off, and the more powerful amp will be more competent at higher volumes (yes...I know, master of the obvious) but the tubes were more tonally balanced, thus the trade off.

I personally have never auditioned an integrated in that price range...I have capped out at about $3K. I don't have an honest POV on whether that PrimaLuna is worth. I did listen to a PrimaLuna integrated (unknown model) driving my rather warm Revel Performa3s. I didn't like it but it was a very warm amp driving a warm speaker. I would think the PrimaLuna would complement the GoldenEars nicely since they are neutral.

If you are willing to look at less powerful amps, I would toss in the Rogue Audio Cronus Magnum II as it has a greatly improved internal phono stage. It isn't at the same level as the Prima-Luna. This is arguably the Gem of Rogue Audios line with a recently improved Phono stage. At $2495, you could get an awesome tube integrated and a turntable and DAC for right around $5k.

This is the difficult but fun part of this hobby. What I would do and what matters to me is completely different than what will matter to you. Good luck.

I suggest the Creek EVO 100A amplifier for your system. That will be a very nice upgrade, and it has plenty of power to run almost any speakers. For $2195 it is a good value.

The turntable is not bad, but an upgrade to the 2M Blue cartridge will be very satisfying.

I also strongly suggest that you get the Musical Fidelity V90-LPS phono preamp; a big improvement for a very modest price.

Put all those upgrades together and your system will be totally transformed,, for less than $3000 total.