Read The Audio Critic, and you will realize that amps, preamps, CD player, DAC, and wires don't make any significant difference at all. Processors (EQ, DSP), speakers, and room acoustics will make a difference.
So in your case, between the speakers or AVR, the correct answer is the speakers.
Bring the same songs that sound harsh to audition the next speakers.
Try Infinity, JBL, Revel, KEF, Dynaudio, Thiel, PSB, Paradigm, Energy, NHT, Salk, Ascend, Philharmonic, Aperion, EMP, RBH first since they are accurate speakers. If you don't like them, then try B&W, Martin Logan, Vienna Acoustics.