Hi,
Good speakers and a well treated room make the biggest impact secondary to simply good source media to begin with. The amp and dac and stuff involved have the least effect overall, but matter of course. At the budget level, I would put everything towards the speakers. Your stereo receiver is plenty good for almost anything in a fairly small room like in an apartment, so you should be fine there.
Overall maybe you might benefit best from and equalizer or DSP of some kind, not sure what your receiver is capable of there, but a simple equalizer may help a ton to tame the treble to avoid fatigue perhaps. I'm guessing you're turning it up to hear the mids and bass more and the treble just stings (again, just a guess, not trying to imply anything). So perhaps you would like the results better if you could just tame the treble. You could try to do this with room treatment, to an extent, but ultimately a little equalizer could be a good thing to try for this if this is more like what you're experiencing.
Otherwise, there are excellent budget speakers that are not bright out there. Just need to know your max budget and where you can buy from.
Very best,