Moving to separates

@gkelly If it is bit-perfect digital all the way to the Integra, how would the source make any difference?

skeptikal,

"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 hear you. My Trinnov is very good as an AV preamp, but not for 2-channel.

Regarding the source...why don't you try to get a home audition and see if it makes a difference in your system?

I do need video so an integrated amp is not in the cards.

You would still be using the AVR for video/multichannel and the integrated would take over for stereo, and you could toggle between the two with the push of a button.  But if you need/want the Dirac for 2-channel as well then yes you couldn’t use an integrated amp.  By the way, if it’s still available this McCormack is an excellent 5-channel amp and is a screaming bargain at the price. 

https://www.usaudiomart.com/details/650104997-mccormack-dna-ht-5/
 

I am in no ways, smart enough to explain to you how a bunch of computer Nerds, who happened to like music. Were able to take a bunch of wires, capacitors, Diodes, transistors, toroidal transformers and put it in a box, mix it all together with some fairy dust To get glorious music to come out of it. I have no clue 🕵️. But apparently they have and and all I can say is thank you very much for your contribution to society.

… but an amp is about the only thing that seems reasonable

High-end audio is a small niche market above box store offerings, and can get very expensively “unreasonably” quickly. For Sonics, the entire audio chain matters: including source(streamer+DAC), preamplifier, amplifier, speakers, and cabling.

While the OP seems to have a great surround system, simply switching from the internal Integra amp to an external amp will have limited effect as the rest of the audio chain will likely limit Sonics. Usually it’s much better to split surround and 2channel audiophile systems as it’s extremely difficult to lift 2 channel Sonics to satisfying levels.

So to answer the OP’s question a better amp would likely be sonically better, but trying to squeeze great 2 channel sonics from a surround system is extremely difficult as better 2 channel components simply perform better.