Moving to separates

I made the jump years ago by going from an AVR to an amp driven the AVR, then to a combo dac/preamp which bypassed the avr entirely, then to a pre and dac separates.  . My avr was not as good as yours. The biggest gain to be had is getting the avr out of the two channel system entirely (although I still have an AVR for HT use and use the external amps and speakers for HT, but the AVR/TV is off for two channel listening). The DAC and pre in the AVR are good, but not as good as well selected separates. Several small steps result in a big step. Honestly, you really need to try it and see how it sounds to your ears on your speakers.

BTW, I admire your room treatment and the effort you put in to improve your room before spending on electronics. I need to do a better job at that.

An AVR contains EVERYTHING in the same box, hence the inevitable close interaction between all the parts in it. Separates do just the opposite, separating all the parts so there is no negative interactions. The result should always be a purer, cleaner sound as long as carefully assembled with adequate cabling. It's expensive and  time consuming to build but plenty worth it imo.

The best is to decide what your long term plan is. For me, I have two main systems. My stereo system and my home theatre system. I went to separates for both of them a long time ago and I stick to A/B amps. For example, in my home theater, I upgraded my pre-amp twice, and my speakers twice, but, the old ADCOM GFA-5503 three channel amp, and the old ADCOM GFA-585LE 2 channel amp from the 90’s are still in service - but, I did have to service them because of their age and some leaking caps. If you plan to go separates step by step, then, using your AVR as a preamp, and starting your journey with amp separates with a lot of power that you plan to keep for a super long time is for me the correct way to start. This is exactly how I started with my stereo system. I bought the one ADCOM 585LE and used my old Sony Receiver as a preamp. When I build my first home theatre system, I moved the ADCOM 585LE to the Home Theatre and bought a matching 3 channel amp. In the mean time, I decided to go to two McIntosh MC275 tube amps for my Stereo, etc.... So, separates can give you a lot of flexibility - especially with amps, which you can keep for decades. 

I don't plan on replacing the Integra any time soon.  It's the flagship model, the DRX-8.4.  It has Dirac, which works wonders.  And it sounds really good.  I don't do vinyl, source is digital (my computer), and I do need video so an integrated amp is not in the cards.  Haven't added or upgraded anything in 8 months so I'm feeling the itch, but an amp is about the only thing that seems reasonable.

How about you dump that computer as your digital source and look into INNUOS. https://innuos.com/pulse-mini/
getting a dedicated music streamer can be a real eye-opener.

Nice listening room you have there.