Stumped, no. The issue may have nothing to do with the cdp.
It may be cables (very possible), and it may be the aluminum dome tweeter (also very possible). Of course, the cdp also might contribute.
Let's assume the speaker is not the issue, since you achieved some diminishment of the sibilance when using upsampling. If the sibilance went away but the clarity suffered then likely a good solution is available without touching speakers. Personally, I do not prefer aluminum dome tweeters as they sound harsher to my ear than cloth dome; I prefer ribbon tweeters the most. But, for the sake of argument, let's assume the speakers are ok.
There are three immediate considerations:
1. The CD Player is possibly the issue.
2. The amp is possibly the issue
3. The Cables are possibly the issue.
I'm not going to get into room tuning; I do not see that as the primary issue here based on your pics.
Solutions (some easy, some tougher):
1. roll the tubes in the cdp; see if changing them yields a substantively softer sound in the treble.
2. Change the ICs from cdp to amp. It's very possible that you can greatly diminish the sibilance. I'm familair with the Harmonic Tech cables. Try a Magnan Cable IC for a change. If you have a serious issue of sibilance, then get the Magnan speaker cables as well. It's going to be "softer" on the high end, a touch more laid back, amazingly like putting tubes in the rig. You may like it quite a bit.
4. Get a tube DAC and use the cdp as transport.
If the tube rolling/cable solutions don't work, then it's likely that you have to reconfigure the components. Big assumption again, but assume your amp is ok. (Frankly, that's not a perfect assumption as the amp is class D which I find can be a tad strident in the treble, but we'll give it the benefit of the doubt (especially if you have used it in other rigs and found it acceptable)
You then would need to try a preamp or a tube DAC. Yes, a pre, even though it may absolutely diminish clarity a hair. Disc player straight to amp for me the times I have tried has been harsher than with pre. The pre will condition the sound and usually "plump" it so as to make it more palatable. But, not all pre's are created equal...
-Of course this is adding another factor or two with a component and cables.
My guess: Tube rolling won't make enough of a difference, but ICs and speaker cables can. If that doesn't do it, then you're looking at changing your cdp, getting a pre, or getting a DAC.
You could add a Tube DAC and use the cdp for a transport. A sweet tube DAC will usually soften a tough transport's high end to some degree. Even cheap cdp's (i.e. Oppo) can sound ok with a good tube DAC. With a good transport a tube DAC will have a good chance of sounding lush.
If it were me, knowing how much cables can tune the sound, I'd do the cable exchange first (and if that doesn't do it, then rolling tubes likely wouldn't have either), then consider a tube DAC.
OR you could take a crap shoot by asking everyone else what cdp is mellower than the Cary. However, demanding that it have volume control will severely curtail your options, you must be aware. I asked that directly when I had the Ah! Njoe Tjoeb tube player and wanted the next step. I was told by several people that the Rega Planet 2000 was more tube-like, and it was. So, if you get several responses which confirm it, you could just swap cdp's like you're hoping to do.
But, watch out, you may be frustrated with a cdp which is warmer but not as detailed as you seem to want. Catch 22. That's why if it's a tonality thing, I'd work with cables first, as they would alter the electronics the least while still giving chance to lose the treble toughness.
BUT, that might not cure the problem. You may have to go through some of these other steps anyway.
Isn't solving sound issues FUN? ;)