Based on reviews the A6 DAC is "not bad", however it is worth trying an external DAC, use the USB - not the IIS. USB will outperform coax or Toslink - except perhaps for the most expensive Aurender streamers, with a perfect Coax cable..
The IIS connection would use the clock from the A6 and since you are upgrading the new DAC's clock should be better. USB uses the new DAC's clock, IIS uses the source's clock. USB cables are less critical as the data is buffered and clocked by the DAC. IIS cables are absolutely critical as the clock is sent from the source so any jitter generated by the source and the cable are passed into the DAC's processing.
For example the Benchmark DAC3 B is sub $2K - I suspect very transparent and well engineered.
However, another thought is to try the Eversolo DMP-A8, this has a much better DAC than the A6 (according to reviews) - and you can sell the A6 for a few $100s. i have an A8 in my 2nd system and it is rather good - I tested it in my big rig in place of my Esoteric K-01XDSE and was impressed.