Basic Questions

Yamaha is my favorite mass market AVR for sound quality and reliability. Bad news it’s it’s still an AVR and thus its 2-channel performance is compromised and greatly holding back what your nice speakers are capable of. And, the only thing worse than the amps in your AVR is the critical preamp section, so both need to be replaced and as mentioned above the easiest and most cost-effective way to do that is with a good stereo integrated amp. And if you’re into vinyl you’ll likewise wanna upgrade your phono preamp as that makes a huge difference as well. Adding these two components into your HT system will absolutely transform your 2-channel performance and probably remind you a lot more of what you heard when you auditioned your speakers.

Before getting into how to hook this up, which is absurdly easy BTW and we can discuss that later, the most important thing now is to share what sound characteristics are most important to you and what improvements you’re looking for over what you have now. That’ll give us a much better idea of what to recommend for your particular goals/tastes/system. With your budget you’ll be in great shape, and you should be very excited for the significant improvements you’re in store for.

Just to maybe calm any fears/questions you may have about hookup, it only requires one additional interconnect if using and integrated amp (two if you get a separate amp/pre) and the stereo amp is hooked to your front L/R speakers. The beauty of this configuration is that you can switch between HT and stereo with the push of one button, and in stereo the AVR will be completely out of the signal path so it’ll be pure 2-channel audio as if you had a completely separate stereo system. Hope this helps.

Have you tried just optimizing the speaker placement in the room?  Moving them away from the wall,  putting them closer together and then further apart,  adjusting the angles.  It may not work within your lifestyle but until you have the best sound you can get with what you have you won't be able utilize what different components can offer.

Have you tried a sub?  It does a lot more than just add bass.

If you are happy with your present system you don't need to change anything.  The reason to add a pre/amp or integrated is for the HT passthrough feature.  You could then run your two channel sources through the new pre/amp equipment instead of the AVR.  For the HT front left and right you would need a pair of interconnects to run from the pre/out L&R of you AVR to the new two channel set up so you can watch movies.  Then you would connect your turntable, streamer/DAC etc to the analog "in" connections on the new equipment.  Not sure about Yamaha but some AVR's convert everything to digital.  So you could run HDMI from your Oppo to AVR for BlueRay movies and use the analog out on the Oppo to play CD/SACD on the new equipment.

The new amp would be a two channel amp and power the front left and right speakers unless you really changed things by getting an AV controller with a new multi channel amp like for example: McIntosh.  A very expensive solution.

Another option to try and improve the sound quality could be to get a more expensive AVR with an in home, risk free trial.  Hope I have answered some of your questions.

I think I'd look for an integrated stereo amplifier with a home theater bypass that would allow it to function as the power amplifier for your home theater setup while operating independently for stereo listening.

I tried to go that route with a Cambridge Audio Azur 840A (just didn't like the sound) and then Krell S-300i, but found my Pathos Classic One Mkiii to be superior to the Krell so am using a custom speaker switch that allows my speakers to be connected to either my home theater receiver or the Pathos.  It's not elegant, but it's functional.

I'll keep it simple. The levels of equipment performance are: Receivers, Integrateds, Separates with stereo amps, then Separates with mono amps. The better your preamp is the better your system will be. 

P.S. The Parasound A21 is a fine amp.