How to proceed?

@decooney

Thanks for your suggestions. They make sense. Unfortunately, I do not have any unused gear lying around and don’t know anyone who would loan me the gear.

One exception-- I tried my old tubed Joida CDP as a transport and the sibilance was worse.

@stuartk my understanding is you have tried different cables between dac and amp and that didn’t solve the issue. Those were DH Labs cables. 
In my experience DH Labs cables are brutally honest and lean slightly on a brighter side of neutral. 
I will give you an example from my most recent cable swap/upgrade experience…

I was using Acoustic Zen Absolute Copper XLR between the Bricasti M3 DAC and XP22 pre, as well as between the XP22 and X260.8 monos. 
The AZ Absolute Copper were a bit too warn for my system with the latest upgrades. So I called The Cable Co and tried the following: Audience AU24SX, Analysis Plus Silver Apex, Kimber KS1126. I had on hand AZ Silver Ref II and the Nordost Tyr 1 and Tyr 2 that my friend loaned me. 
There was a significant increase in sibilance with the AP Silver Apex. A bit less with Audience AU24SX but still present, there with AZ Silver Reg but no sibilance with Kimber and Nordost Tyr 2. I never experienced sibilance in this system with the AZ Absolute Coppers. There was always a super smooth midrange with delicate treble but the bass was too plump with my Wilsons and the Pass monos. I struck gold with Nordost Tyr 2 XLRs. My speaker cables are Audience AU24SX 

So the moral of the story is - you still have not done due diligence with the cables. 

@audphile1 

Thanks for your suggestions.

I have used The Cable Co. in the past and felt very positive about them but my last experience was so negative, I'm not sure I'd want to go back. 

I had A. Zen Silver Reference and they worked great in my previous system but were too bright once I acquired the Hegel and Jay's. So I tried the Absolute Copper but they were extremely dark sounding, top to bottom. 

I'd be very happy if my problem could be solved via cables.

AZ Absolute Copper are warm. But don’t forget with higher resolution components like your Jays cdt and Aqua DAC + H390 that may be a welcome change. I ruled your speakers out - there’s nothing there that will give you that sibilance.
If you can, try the Nordost Tyr 2. Used they’re not terrible price wise for the sound upgrade they bring to the table. You can sell them if they don’t work out but I doubt that will be the case. They’re excellent cables. Much more refined top to bottom than the older Nordost lines which I wouldn’t recommend as a remedy for brightness and sibilance. 

How old is your Aqua? Chances are it won’t change too much but most times I’ve found DACs do change after 400-500 hours run time (though in my case they usually got a bit more detailed). But if it’s new you may want to run it constantly for a few days just to see if anything changes. If I recall correctly I think in one review of the La Voce the reviewer found it a bit strident on the top end compared to some other DACs. I know you said you didn’t want brand recommendations but you may want to look at Mojo audio DACs based on what you said about the Hegel vs the Aqua DAC. They have nice organic tone but are not rough on top at all, and mine sounded best when run from a good transport.