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.