I have commented on Chord Etude a few times in Head-Fi. I think my mind has changed slightly since I first got it in October 2018.
The first thing I would say is that I see you're using Chord integrated amplifier 2650. Hence, the sonic limitations would be as much due to the preamplifier section of the 2650 as the amplifier section. As a result, to get the most out of Etude, you really need to connect DAVE directly to Etude. Otherwise, you'll lose transparency. Obviously, if you have a vinyl setup, that would be a challenge.
The second thing I would say is that if you like Chord 2650, Chord Etude is probably the right upgrade for you. I think different amps sound different. Some amplifiers are built to sound neutral (Benchmark AHB2, Bryston 4B3, Chord amps) while others tend to sound warmer (maybe not as warm as tube amps) where they introduce euphonic 2nd and 3rd harmonic distortions but inevitably with tradeoffs to microdetails, microdynamics and transparency. For me, I never bought any older Chord amplifiers because at shows and showrooms, I have always found the older generation of Chord amplifiers to sound slightly harsh at times, despite their neutrality, transparency, microdynamics and macrodynamics. I have not been able to hear the Mk II versions of Chord amplifiers but am lucky to have the Chord Etude. I think my summary would be that Chord Etude preserves all the wonderful qualities of the older Chord amplifiers but there is a beauty and smoothness to the sound when it's meant to be warm and pleasing, meaning that the harshness I didn't like when I hear in the Mk I Chord amplifiers are gone. But when the music is meant to be harsh and dynamics, Etude can give you that power and oomph just like the older Chord amplifiers. Most importantly, I find the transparency, micro- and macrodynamics are still completely preserved with Chord Etude. I have to admit I have always found Chord amplifiers to be extremely fast so I really am not sure if Chord Etude is any "faster" than the Chord 2650. And I have not had any in-home demos of other neutral amplifiers so I cannot definitively say they can't be better than the Chord Etude but for me, the other amps often sound a little harsher than the Etude but I may be biased by the look of the Etude because it matches my DAVE and Blu2.
I think I would only have one caveat on you getting the Chord Etude, which is that when I used to drive my speakers with Sanders Magtech, I would recognize that when listening to DAVE with headphones, there is a difference in transparency, microdynamics, harshness but I just kind of accepted this as reality so over time, I was able to ignore the difference between speakers vs headphones. When I got the Chord Etude, the upgrade was so significant that I started believing that the Etude through my speakers are as transparent as DAVE to my headphones. Or at least the difference in transparency was very subtle. Unfortunately, over time, because Etude is so transparent, it actually becomes easier to hear the subtle differences between DAVE to headphones vs Etude to speakers. Yes, the sound is the closest as headphones as I can get so far (and based on other demo systems I've heard). So in many ways, I completely agree with John Franks that it is currently the best amp to partner with DAVE. But with Chord Hugo TT2 being able to put out 8-18W to speakers, I suspect in 3-5 years time, we may see the same technology developed to a point where the DX amps can drive 150W into speakers. When that happens, I guess I can upgrade my Etude then.
