@Eppie
my main focus is the sound quality of the 2 Channel when playing music with my horn speakers, the Volti Lucera, there’s nothing much on tv these days, being retired I have watched every thing a couple times..There is a fine line with horn speakers not coming off to bright, my current Yamaha isn’t to bad but a tad bright…
Pretty much any modern amplifier will measure flat from 20Hz to 20KHz so any perceived brightness is most likely due to other factors. Toeing the speakers out slightly so that they are off-axis from your listening position can help roll off the highs a little bit. The sound is influenced by speaker placement and positioning much more than the equipment. Depending on your seating distance, floor and wall reflections can come into play too.
If you are using YPAO, try pure or direct mode to disable sound processing and see if it is the YPAO processing affecting the highs.
I looked at the specs for your RX-A2060. It has more power than the AVRs mentioned and is a good AVR. Personally, I don't think you would gain much in replacing it. The main difference would be Audessey sound processing vs YPAO. Audessey tends to work better than YPAO. Some don't like the surround processing and just leave it off, If you have manual EQ you can try some manual tone adjustment.
Horn speakers are very efficient and don't need a lot of power so the A2060 is more than enough. If you happen to like the Pass Labs amp, note that you can use the pre-amp out on the Yamaha to drive the Pass Labs amp for the main speakers. You would need to run YPAO again because the power level from the Pass Labs is different from the Yamaha and you will need to level match the centre channel and surround speakers to your mains, or level match them manually. I think you should experiment with what you have before buying a new AVR.
@AcuDefTechGuy is familiar with Yamaha and can correct me if I'm wrong here.