Fun question. My vote would be a two channel integrated amplifier. Something simple that does NOT have an integrated DAC or phonostage - just pre and amp
Right now, I don’t think you will be able to hear the difference if you put more $ into the phono rig, given the limitations of the Yamaha A/V receiver for 2-channel listening
System quality needs some balance across its components, and your phono rig seems well thought out, already - a solid setup
For $2k, you’ve got great integrated choices, new or used. Looking only at “pure” integrated amps (without DAC or phonostage) will help narrow things down quite a bit
Amp may seem less exciting now, but will make a big difference and be the foundation for a TT upgrade later
Let us know what you audition!
Have a great day