The mac mini seems to be widely used
Widely used is not the same as something being ideal but that is a side issue if the changes have just happened recently. I thought you meant that it wasn’t working well with your new DSD from the start.
Running in shouldn’t make such a massive difference and it is unusual it would make it sound more harsh - usually it is the other way around.
If you are 100% sure this “glare” wasn’t there before, then the only conclusion is that something has changed within your system.
What I find confusing is that you say some music still sounds fine - if this was due to some kind of change in the system then it should be present for everything. It should not be music dependent.
Is it possible that the “bad” sounding tracks are in a particular format? For example poorly recorded lossy audio which sounds good on less revealing systems can sound terrible on higher end equipment - simply because you can hear all the inadequacies in greater detail. Although it wouldn’t make sense that these sounded fine before and don’t now.
Otherwise that leaves a lot of variables. You have the mac mini, the DAC, the cables and also the power supply. For example your DAC and Mac Mini may be fine but it may be that one of your cables is picking up some radio transmissions that the DSDac is sensitive to.
It may also be that there is something running on your home power supply (or even your street supply) that is degrading your sound. Have you installed any new equipment that may be responsible?
Might be worth checking all your cables are properly connected and if you have alternatives try swapping them out.
Also if you have another computer to try (not necessarily a Mac Mini) it might be worth using that to with the same tracks to see if the character you describe is still there.
Finally it is also possible a fault with one of your amps is doing something which interferes with you DSDac but not your old DAC. I understand this is unlikely but do you have other amps you can try it with - obviously this will change the character of the sound, but presumably if it is some kind of fault with the DAC any decent amp should be able to reveal it.
Beyond that I’m not sure what you can do yourself.