In my experience - the transport is where it’s at - DAC comes second. With a better transport comes a better sound and edginess becomes less and less. My guess is that your DAC has much much more potential.
In my very recent experience I connected (or a competent dealer did) my cheap and somewhat edgy Metrum Octave DAC into a Grimm Audio MU1 digital front end - this totally transformed the Metrum for the better.
In a similar fashion I also fronted my DAC with a dCS Network Bridge which again took the edginess of my DAC (in fact DACs - I also have an AN 0.1x).
If I were in your shoes - I would certainly - without doubt - upgrade your transport and not your DAC.
Or, just go buy a dCS Rossini APEX (DAC and streamer) and be done with it! That thing sounds stunning.