How to proceed?

@stuartk This thread has really gotten going! Sibilance is such a multi-caused problem, that if I were you, I'd try a process of elimination approach that causes the least disruption. @alexatpos is on to something very important with (a) positioning. If you're in a constrained space, do what you can to ensure that you cannot fix the problem with positioning before (b) trying cables to change the problem. If that doesn't work, (c) an equalizer would be a very effective and flexible tool but if that's not possible, then (d) seeking a warmer power source (at least as an experiment) would be the ticket.

I had fairly bright standmounts and a solid state A/B amp (a fairly robust Atoll IN200 SE)  was too bright. I brought in a Pass XA-25 and while it didn't cure my problem -- because I had Beryllium tweeters -- it helped a lot. A Class A amp is an easy way experiment, not least because if it works, you could sell your Hegel and probably not lose much money. 

@stuartk You have a really nice system. That Aqua DAC seems really high quality and is R2R. I see good arguments in other threads that the DAC might be the problem. I find it hard to suspect the DAC, as it's well made and is R2R. Of course, if it's the DAC, that's a simple one for one switch.

If do wonder about the Hegel and (maybe) the room acoustics. Is there anyway you can borrow another amp to try out to see if that changes anything? If you tried an amp that was definitely on the warm side, you could really know about the Hegel. Looking at your room, I see there's not much about acoustics you can do that's easy. 

There is a nice discussion here -- some really good posts -- which indicate that room acoustics likely won’t solve it, though there is some debate about that. Some more discussion here, mentioning EQ and toe-in, among other ideas.