You are at the stage that splitting the functions may be appropriate. Given where you are… there is lots of opportunities for improvement in both functions… and it sounds like over time you are likely to take advantage of them.
My rule of thumb is to always at least double the price in an upgrade… more if possible. You want to set yourself up for a real “wow, that sounds a lot better moment”. So I would recommend spending $5K or more on a DAC.
There are lots of good DACs… especially used at that price. I don’t see that you have posted your system under your user ID… that would be useful. I have been shocked at how good Audio Research DACs are… and have been for more than 20 years. My first choice would be a a used Audio Research Reference DAC. Incredibly musical and detailed.
There are lots of other good quality DACs available. You want to get one that matches you aesthetic. I would not get anything older than five years or so. DACs… and streamers for that matter, have made big advances over the last decade. Berkeley and Linn are companies I would look at.