... I use for music and movies.
... the Arendal 1961 towers prefer twice the watts of the NAD to really perform.
The NAD has 150 watts per channel which should be enough for the 87dB Arendal speakers
and you have a sub so loudness should not be a problem unless your listening room is huge. What you don't like is the Class D sound, I generally find Class D lacking too.
Preamps that include a phono preamp, HDMI and a DAC are rare. The
Bryston BR-20 preamp has an excellent DAC, HDMI inputs and single ended inputs so a phono preamp can be plugged in.
And the Bryston blows the budget so I need to re-think this...
The AVA DVA SET 500 would add just a hint of warmth and bottom end which your speakers would appreciate and leave more room in the budget for future upgrades. Unless you are thinking of getting the DVA Digital Preamp/DAC. The DVA225 amps would be a perfect match but the DVA A2D analog-to-digital converter would be needed for the phono preamp. And then there is the question of HDMI input.
Keeping the budget below $4000 leaves only $1200 for a preamp, DAC and phono amp after buying the SET 500. You might be able to achieve a step up in quality buying used.
The Vision RB preamp with Vision phono, a SET 500, an affordable DAC and a 4K HDMI to Audio extractor would be a huge improvement.