I checked out your system page to get an idea of your room- beautiful house! Your options for speaker placement don’t seem to be working in your favor though.
The open doorway behind your left speaker and the right speaker almost in a corner are enough to cause issue. Not sure how WAF plays into your situation but have you considered rotating your monitors 90 clockwise?
I doubt the sibilance your experiencing is a by product of your dac (assuming it’s in perfect working order). I believe the La Voce (while producing a very good presentation) is the warmest of the Aqua line when it comes to high frequency reproduction. I have the La Scala Optologic MKII and I’ve never noticed or felt the presentation to be sibilant (outside of what might be within a particular recording). I also believe purchasing a Border Patrol would be a step backwards in your case.
I cannot comment on how the dac within your Hegel plays into this but I would definitely wager that it is not of the level of quality of your La Voce. While I cannot speculate as to what it’s doing differently in this case my guess would be that its presentation is just more rolled off and less transparent than that of the La Voce (but again that’s a guess). Any higher quality dac you purchase will probably present the same issues but with more magnitude.
Just as an experiment have you tried placing light acoustic materials around the various surfaces in your listening room just see what effects it may have?