Would adding a Dac improve the sound for my setup?

After looking at your system and seeing your goals, (clarity and soundstage)my advice is to forget the dac, scrap the PS power conditioner and pick up a good power conditioner, such as an Audience AR6, or the 6T if you can stretch. Lower noise floor and overall sound improvement, IMO. Of course I can't diagnose your system without hearing it, but neither can anyone else, so my opinion is as valid/ignorant as anyone else's. Again, IMO, a $1000 DAC is just a sideways move. If you want a real improvement over the AA, you will have to break more eggs than that. At least that's what I've found. Good luck.

Musical Fidelity V-DAC for $299. You can return it if you don't hear a big difference; I think you will. Use a decent digital cable.

Adding the right DAC can improve all the sonic signatures you're looking for. But, like everything else, it is system dependent.
Burson dac is the one I would highly recommend.
There is a 30 day trial for the Burson. I don't think you'll be sending it back though.

The Wyred 4 Sound DAC-1 would be worth considering and is in your price range. I believe it would be a step up for you.

Ask yourself this question. Do you find that the music (sound stage) becomes compressed as the size of the music increases (more instruments) and does the sound stage become congested as you turn up the volume with larger scale recordings? However, when you play small scale recordings, trios, female vocals without much instrumental support behind them, the sound stage is good, well defined, etc. . .

This is your CD player. I cannot tell you if it is the DAC portion of this player or what aspect. But the AA Primo CDP has this fault. I bought one when my AA Capitole needed to be repaired and figured the Primo would give me similar, but not as good perfomance. It was fine with small scale music, but fell apart with larger scale music.

While I hate to say this to you, my recommendation would be to dump the Primo and get either a better CDP or even one that may have digital inputs. You can try a DAC, but I don't know if it will fix the problem with the AA unit or not.