Upgrade path question with $2k to spend

If you are using the bult-in room correction, plug your main speaker's ports and run it again. :)

In general though, I have not heard Yamaha HT receivers in a very long time, but I do know that the quality of the sound processing, especially the DAC's of HT processors is really very wide.  The gap among products is really disappointingly wide, when you'd think it should be really close.  So, generally speaking, I would encourage you to try out an Anthem if you can find one, only because they sound good and relatively inexpensive.  For sure, not Onlyo or Emotiva. 

lyngdorf tdai 1120

This is hard. I would immediately look to a phono stage… $2K will get you a much better one. The Phonostage is far up in the signal chain… But, first thing has to be the Yamaha. Surround processors sound terrible for two channel audio. I would trade it in and apply all your cash. I would buy a used integrated Luxman or NAD (only preamp and amp)… reach as high as possible. If you can actually get a used audiphile piece it will raise the performance level so much, it will allow you many years to get a better phono stage… which will then make a huge difference. Then TT and cartridge.

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.