As I fellow senior music lover who, like the OP, also has tinnitus, let me say this. Your tinnitus most likely becomes an issue with brighter presentations and higher volumes. No matter what DAC you get, you will still find certain recordings an issue. This is because of the way the music was recorded/mastered/remastered, etc. In other words, the effect of human input and the sonic signature of the gear used in the music production/recording process before it even gets to be on your CD/ or digital stream.
So here’s my input. Buy a good quality equalizer like a Schiit Loki and insert it into your music chain. Eiter between your preamp and power amp or your DAC and preamp. It is very transparent yet will allow you to modify the high and middle frequencies to suit your specific hearing preferences on a global as well as a recording by recording basis. This little inexpensive device may get you further towards your goal of making your digital source more listenable than what tonal flavour DAC you get. It has a bypass switch so it can be in the chain when you want it. Not saying you should not get a DAC as a better DAC regardless of the technology will get you closer to the music than the internal one you are using, but the ability to adjust tonal balance, for me was the best way to make music more listenable with tinnitus.