Well, live music is pretty "bright", if it has cymbals and other high frequency instruments. The key with an audio system is to retain a natural brightness and "air", without harshness or distortion in the highs. Based on personal experience, I would agree that using a separate power amp with an audio video receiver is not likely to dramatically improve your audio quality, unless your current speakers are causing the receiver to go into clipping. I am currently using a Denon AVR as a pre-amp, running it into a Krell class A power amp. I do believe the Krell improves on the "musicality" of the sound a tad, but I'm still not happy with the highs, in that they are not as natural, open, and "airy" sounding as they should be.
I would also agree that better speakers will lead to the biggest changes in your sound. But, to even get bookshelf size high quality speakers is expensive. It's a tough situation. As stated above, room reflections can also be a source of "harshness" in the highs, so room treatment should be investigated.
What I am now looking into is getting a quality pre-amp that has a home theater bypass, so I can still use my AVR for movies but also get improved two-channel sound. I would connect the pre-amp to my Krell power amp. The Parasound Halo P5 is my current leading candidate, as it is a "jack of all trades" and not terribly expensive, but I don't really have a place for it now in my rack. I'm working on that, however.
Also, you didn't mention what cables you are using. Many will tell you that more expensive cables are "fairy dust" products and that you cannot hear the differences, but I can easily hear the differences in sound between cables. The more resolving your electronics are, the more difference you will be able to hear between cables.
In your situation, I think I would first research and get some high quality tower speakers that are appropriate for your room size. There are scads of options. Also find out how much room reflections you are dealing with, and see if you can treat those somewhat. Then, at that point, you can see how things sound. Then you can always continue research on an integrated amp so as to improve those highs.