I think the Hegel H90 would be a nice upgrade and offer the characteristics you're looking for. There's one available used a little above your price target, but I think you can get him down closer to $1100, and frankly it's worth the stretch if you can swing it.
There's a Soundstage review of the H90 where the reviewer compares it to an NAD C356BEEE so thought it would be particularly useful for your frame of reference. Here's the comparison section...
In comparisons with my NAD C 356BEE integrated amplifier ($900) with classical music, the H90 generally opened up the sound to something more like the enveloping acoustic of a concert hall. The soundstage was given greater dimensionality. When I switched to the H90 from the NAD while listening to Mahler’s Symphony No.7, with Claudio Abbado conducting the Berlin Philharmonic (CD, Deutsche Grammophon 289 471 623-2), I felt as if my seat had been upgraded. The brasses packed more punch; the bass and low midrange exhibited greater dynamic control. Where the NAD provided more raw power, the Hegel did it with finesse, pushing forward details in the first movement’s march for full orchestra. At the same time, isolated mallet strokes on timpani and bells decayed naturally, and were imaged distinctly. The Hegel’s key advantages were in dynamics and details.
I thought it interesting that the improvements were similar to what you're looking to improve in your system. Anyway, here's the whole review FYI...
https://soundstageaccess.com/index.php/equipment-reviews/859-hegel-music-systems-h90-integrated-ampl...Hope this helps, and best of luck.
