Don't concede defeat before you've even fought the battle. Your receiver is 80W/channel at acceptable distortion thresholds. Your speakers have 87dB / 2.83v / meter sensitivity. At 80 watts at your seating distance, the SPL of your towers will reach about 92dB according to
@lovinthehd's linked calculator. That's the SPL of a busy freeway, or about 20dB louder than a noisy restaurant. Listening at that level for 8 hours could cause hearing damage
according to this chart.
It doesn't take a lot of power to drive speakers of typical sensitivity to annoying levels. I think your system volume will be limited more by your subwoofer than by your AVR, and that's a pretty decent subwoofer. And if your AVR were rated at 120 watts instead of 80, you might squeeze out another couple of dB -- a difference that would be all but inaudible.
I say keep your current AVR. Don't get too hung up on electronics. You're sorely mistaken in your belief that your AVR is the most important component in the system. It's the speakers that make the sound, and good sound comes from good speakers, not expensive electronics or boutique cables.