I'm with @russ69  on this. You have a mixed starter system now. The mix is the Yammy HT receiver in with 2 channel.. I like the Yammy's quality and sound And they make decent integrated also which is what you need . There are different priorities between the 2 channel and HT.  BTW, A 2 channel HT is fine for me and many others who have used it. .If you are adventurous a tube integrated may sound better to you also. But expect a little maintenance IE tube changing when bad. But many will last 5-10 yrs so its not an extraordinary amount to maintain. Then after the amp, the turntable needs upgrade. Then the phono preamp. Cartridge is alright for the time,have fun

How is the TT mounted, there is room to improve the presentation from it and not too much money will be required if a DIY approach is tried.

Trialling a Few Platter Mat Materials will usually have a cost attached if a few loaned ones are not able to be arranged. Exchanges of Mats a can also produce one that can have a real impact in uplifting the SQ.

A Phonostage can be considered, a shop demonstration and home trial is worth trying to arrange, I don't suspect this will cost much money to achieve.

I really don't see how my $2,000 Yamaha running in pure direct mode with 200wpc is affecting the sound quality.  Who cares if it can do 13.2 I'm running it in 2.1 or 2.0.  I was thinking going emotiva xpa 3 for a power Amp for my fronts and then I'd be able to run a Dirac Live setup.  Still feel like my TT and cart are the weakest links

Upgrade path question with $2k to spend

I really don't see how my $2,000 Yamaha running in pure direct mode with 200wpc is affecting the sound quality.

The question then is this, Why do you want to spend $2k  to upgrade a sound system if all sound is equal? Do you really think the priorities for  movie dialog with a few explosions and music which covers 20-20Khz signal are the same? if you want HT then the Yammy is fine. But I've been down that route and it is not the path for good 2 channel. But its your $$ to do as you please

Need to get that Yamaha HT Amp out of the chain. 

2K you get a good used Hegel,