What to upgrade next.

I would invest in a good streamer and external DAC. The Node 2i is a good place to start for a streamer. I really can’t recommend the right DAC as I have just started out on the external DAC journey. What I am using now,I’m sure won’t still be in my systems next year. 

     I would get your streaming situation figured out first,this way you have a better idea of the speaker synergy,and go from there. 
 
      Enjoy the hunt!

What is your main focus? Music? Movies? Both?

Your Denon is for home theater, movies so if your emphasis is on music you will have to do something about that.

Your ordinary desktops are not the best for streaming music unless you have a linear power supply, good hdmi cable. Computers can produce a lot of noise and like you said you have a lot of fan noise.
How are you streaming, wireless or cable?

That being said I use a Intel Nuc running Plex as a music server, though I have not done it yet I can get a linear ps and good hdmi cable for it which will make a significant difference.
I do not know why you are having the Windows glitches, I am running Win 10 with Plex and have no issues.

Your bad copies of MP3s are definitely a sticking point. And what do you mean being replaced to HD audio files? Replaced how? With what?
I rip all my music to FLAC from CDs, the MP3s that I do have I am replacing with CDs.

Will

1st, Others here know about quality streaming, I haven’t a clue.

2nd, Signal

No matter what you change/add, you already know you need to solve your signal. Is your internet erratic due to your location, or can you upgrade to FIOS? Are you using wired or wireless? Wireless today, starting with a good signal can be very good, however, wired is faster, used to be 10X signal strength. So if marginal, try wired. There are also routers with signal boosters using house wiring and dual antennas, the receiver near your device(s) location.

3rd, I think you are talking about using your Home Theater audio system for 2 channel music, correct? Please clarify that for us.

I do know about music thru my small home theater, for many years. I watch a lot of music video 5.1 and 2 channel, via my home theater. 2 or 5.1 Channel DVD concerts, TV shows like the Voice, XFactor, Songland, YouTube... Hard Drive with 3D Movies, ... Netflix, Prime, Hulu, Viki and some limited music streaming via Pandora.

I used a dedicated PC to my AV receiver for many years. Fanless via 5.1 audio on motherboard to avoid heat of separate audio card. And selected for quiet hard drive.

Small wireless chicklet keyboard is very helpful doing this. Originally PC for unlimited internet access, early smart tv’s browsers were very limited.
Now mostly a modern Smart TV, the PC remains for it’s disc drive and hard drive, I don’t but they can connect to home network to access other pcs).

Much content is 2 channel, I often find the cable company/av receiver creates un-natural surround, so I often force 2 channel and find improvement. The point is, when in 2 channel, it is your front, no center, and, depending on your circuit, sub(s) might be on or off. Therefore, go for the best full range mains your physical setup allows, and if sub(s) for more bass, keep them in the system even for 2 channel.

2 channel, no center speaker active, the mains need to be positioned to create/locate a phantom center, specific enough for imaging.

There is a separate thread about great speakers may not be best if too close or using great speakers in too small a room.

https://forum.audiogon.com/discussions/just-spoke-to-an-old-client-of-mine-avantgarde-owner

I take it you like your speakers. I suggest you upgrade your source and also replace the Denon AVR and and possibly the amplifier. That would improve what you are getting from them.

I would start with the purchase of a streamer. The Bluesound Node is within budget. They run $500. The internal DAC is OK, however many replace it with an external DAC of choice.  This you could also consider after getting familiar with the Node.

The 1st question I have, are we talking about a 2 channel system for music?. I believe your Denon and Carver amp are meant for theater use. If so, I would consider selling both the Denon and Carver and purchasing an 2-channel integrated amplifier. An integrated is much easier on the budget than separates. However, you could also just replace the Denon with a preamp and continue to use the Carver amp if it works well with your speakers.

There are many threads here on AG concerning streamers, many specific to the Node, as well as integrated amplifiers. I would be inclined to search these threads.  I would recommend considering the the used market for amplification.  

Good luck in your quest.

 

I agree with @mesch -- if you like your speakers, changing amps, or at least introducing a better preamp, would be very effective. And, as others posted, all of *those* choices depend on your goals and preferences. Ends first, then means.