Would adding a Dac improve the sound for my setup?

Not all rooms need to be "treated". I am in my fourth room in the same house, two have needed treament and two have not. That being said, I agree 100% that if a room does need treatment, there is no better return on investment. Having just bought 8 various types of Real Trap panels (in addition to what I already owned), I can attest that some of these products are better than others, but addressing the room is key.

That being said, I can also state with a high degree of confidence the inherant weakness in the OP's CDP (but also its strengths).

Ok then I'll give priority to room treatment. Unfortunately I can only treat the front wall behind the speakers, because this is in our master bedroom. My wife doesn't want to see too many things. I'll put a artistic panel behind each speaker and start from there.

Rbc
Always remember, it's much more easy to get forgiveness than to get permission.

My wife liked my Ready Acoustic panels so well she made me buy some more when I moved them to another system. YMMV.

I bought the Rega DAC a few weeks ago. It was a huge upgrade over my Rotel CDP. I'm loving it. Some say it rivals the Rega Saturn, but for way less $$$