Soul, welcome. It's highly doubtful in most cases that a "better amp" will provide an audibly significant upgrade. The transient performance you mention is determined by the program material, the speakers and the room acoustics. Any competently designed amplifying device has to have sufficient transient response capability to handle the "fastest" frequencies of interest at the maximum output level.
You don't mention the max output of your present receiver, but the "distortion performance" is inaudibly low at that level, quite possibly less than the speaker or program material distortion. If you actually are playing at extremely high levels creating a possibility of permanent hearing damage, then amplifier distortion on peaks can be a factor. An amplifier with a far higher maximum output(at least 300 watts)is one remedy, but a more prudent one is to turn the volume down a dB or two.
At this point, without knowing more about your present receiver, the suggestion for replacing the Yamaha would be one of the Denon or Onkyo models with the top Audyssey MultEQ XT-32 auto calibration and room equalization.
As to other possible upgrades, you haven't mentioned what your other speakers and sub are, and this might be an area for significant improvement.
