Upgrade path question with $2k to spend

OP,

Surround processors are crammed with all sorts of functions. In home theater you have video distracting you from the audio. Audio only systems do that well. If you want good audio you need to get audio only stuff.

Take this into consideration, the very best audio amps are two boxes… one for left channel one for right. The very best preamps are two box solutions, one for the power supply and one for the preamp functions. The best preamps are a single or double box. Separating each function permits isolation of the circuits and power supply. cramming this stuff and many amps in a bag is not going to sound good. I have a home theater system worth around $50K… it is not remotely competitive in sound quality with my audio system.
 

Ok so how about this then.  I like to occasionally listen to the system loud.  I'm getting 200+ wpc through my yamaha.  The integrated amps I see are not even close to that kind of power. Suggestions?

Having everything separate means having lots more connection points and the various wiring to connect all of it together so a good integrated would be the way to go. The old, worn out thought process said monoblocks, and all the associated stuff to go with them was the way to go but technology has come a long way and modern integrated amps sound every bit as good as separates. 

As for WPC, chances are you never or rarely reach that 200 level and there are lots of integrateds that are rated at 120 or 150 wpc that will play as loud as you want (unless you're playing outdoors or in a concert hall). Peachtree and Parasound are two that come to mind.

Not the 6.

Save a bit more and go for the Rega Planar 8.

You can continue with your current cart and phono stage.

Will be the best bang for buck improvement and will withstand further upgrades downstream.

I used to use a 90's Sony ES, HT 5.1 amp to run my DIY (morel drivers) speakers and sub.  It was pre-HDMI and lacked other now commonly found  features that i needed.  I then started my first dedicated 2CH system with that Sony amp in Direct mode for stereo, and bought a Yamaha AX840 to backfill my HT setup.  It looks to be about $100 less than yours in the same line.  It totally destroyed the audio SQ of those speakers.  It was apparent on the first track.  As some above have also implied, I (personally)  don't notice the SQ issue in HT that much but that's me.  

In my current 2CH I also use the same cart and TT thru a Vincent Pho8 pre.   Using a now newer, tube amp ($4000 msrp) along  with a modded MHDT Orchid DAC for CDs, I feel the vinyl side holds its own very well compared to the well regarded DAC.  In fact both sources sound pretty amazing.  Not being that familiar with your speakers but knowing the brand's reputation it's my experience that your weak link is the power source.  No, I  can't fix the 2CH vs 5.1 issue at that budget but feel strongly your amp is not the 2CH amp your system is needing.    There are a slew of much better 2CH amps, new and especially used, for $2k.  Maybe work the speaker selector device angle harder and run 2 amps?  For the sub, try using the 5.1 from the HT and the hi-power inputs from the 2CH if sub has both?  Maybe others can help here as I've never "shared" a sub like that.