That is quit a dilema. I would guess that you would not be posting unless you were trying to figure out how to achieve some more fidelity from your system.
i am sure you know the first place to upgrade would be the AVR… but you cannot. So, accepting that. I would say that you could achieve better sound with either the Streamer or DAC. Both would be better as they (without knowing what the DAC sounds like… but it is in a very low price range). An Aurrender N150 would be an excellent choice. Also a Schiit Yggdrasil DAC likely a good choice.
Let me suggest something sneakier. Linn makes an excellent DRM. A one box solution that can be a streamer… DAC, preamp, and amp if you want. There are three levels of DAC available. The mid-stream one is excellent. You might get one with the streamer and DAC… while way more than you might want to spend… maybe take some time save up. If you did this, someday, without your wife knowing you could add or upgrade components with no visible changes to the room. Over time you could turn it into a really high end system. I’d have a carefull look at what Linn has.
By the way, you need not know what improvements you want. The one nearly absolute is that better sound is infinitely possible. In the first few decades I quickly learned that better sound was always an upgrade away. It was only after years of listening to other systems I could articulate what I wanted in a better system.