Thought I'll Ask Here, Too... Best DAC/AMP Combo for Sennheiser HD 600?

Sennheiser 560s and HD 600 are two of my favorite headphones so far. I decided to keep HD 600 but I'm wondering if I should upgrade my setup to get more sound quality out of these... Currently using Fiio K5 Pro. The comfortable volume for me is usually at around 11am but I can safely raise it to 2pm when I want more. I'm keeping it on medium gain. Some things I'd like are:
  1. The absolute must is that the sound quality would be significantly better than the one on Fiio K5 Pro. I'm not looking to get 100% performance and my budget is limited, so if some DAC/AMP combo can do like 10% less than the one that costs 100$ more, the cheaper one is fine for me.
  2. Harshness is an issue for me and I feel like Fiio K5 Pro is making the audio more harsh, maybe I'm overthinking it.
  3. Ideally I'd like it to be a USB UAC 1 type of dac/amp so that I could avoid the mini-usb dac I'm using to connect to a game console, deliver audio to the dac/amp and then to headphones. This isn't a requirement but would benefit me.
  4. If UAC 1 isn't an option, I need it to have optical or coaxial (preferably coaxial), so I could use that mini usb dac.
  5. Budget under 500$, the cheaper the better unless a more expensive option is miles ahead. Let's say option A is 200$ and B is 450$, if the option A is 10-20% less quality, I'll be fine. But if there's a major boost, I'll consider... likely won't buy but I'll consider and see if I can save up for it.
  6. Needs to be a DAC/AMP combo and not separate units.
Any suggestions?

Oct 14, 2021
Grace DAC Balanced and THX AAA 789 IMO