Responses from goldprintaudio

getting into streaming
HiFi Rose streamers come with a remote control.....and Lumin has an optional remote control for their units.  Both of these can "technically" do what you are wanting.  But it's significantly easier to use an iPad (or iPhone) for control.    
Streamer/server newbie
Lumin U2 or U2-Mini are great choices.  (I'm a Lumin dealer) But you mentioned "download"....neither of these will have on-board storage, so if you truly want to download cds, you will need a NAS or storage device.  If you only want to stream (Ti... 
Shout out to Revival Audio Atalante 3 speakers
Yes for sure....the 3s and the 5s are incredible bargains at the price.  
Integrated SET...
Cary 300SEI is a great choice.  Line Magnetic has a couple of good options as well (845ia, 805ia).  845Premium as well, but it's a bit above your budget.        
Shout out to Revival Audio Atalante 3 speakers
@gandalf  Glad you're loving the Pulsar2s!  They are fantastic speakers. The Atalante3s had a small price bump since Nonoise grabbed his pair, they are $2595.  
Are Harbeth Super HL5 XD right for me?
I'm a Harbeth dealer......  I don't think you'll have issues with them being a foot of the back wall.  They should sound really nice with your amps!  
Good speakers for Parasound Halo JC1
Soix beat me to it....I would for sure check out the Joseph Perspective2s. They are a nice match with JC1s.  
Shout out to Revival Audio Atalante 3 speakers
Here's another nice review on both the 3s and 5s --  https://www.subwooferstereo.com/2023/03/revival-audio-atalante-3-and-atalante-5.html  
Top turntables under $2k
Nice system!....Cronus and LS50s are a fun combo. You could find a preowned VPI Scout at that price point.  I also have quite a few customers running Rega P3/P6 with a Cronus.  
Integrated Amp Shopping Decisions
I'm a dealer for several of lines you mentioned (Rogue, Bel Canto, Parasound).  The Sphinx is a great choice and very flexible unit with its power output and onboard phonostage. Another option you didn't mention that you may want to consider, the ... 
Something other than Harbeth SHL5
As mentioned above a couple of times, the Joseph Pulsar could be a potential option if you would be ok with a stand mount (and they for sure do not sound like a speaker in a shoebox). Another potential option you might want to check out is the ne... 
Bel Canto E1-X Dac
I'm a Bel Canto dealer.....do you have specific questions on the E1X? Taylor www.goldprintaudio.com    
Shout out to Revival Audio Atalante 3 speakers
Yes, they for sure have a huge sweet spot.    
Shout out to Revival Audio Atalante 3 speakers
That's almost the exact same level of toe in that I've been using here with both the 5s and the 3s.  Just a small amount seems to be about all they really need.  
Shout out to Revival Audio Atalante 3 speakers
They look really nice in your setup!