My first recommendation would be getting rid of Airplay streaming through the Hegel. My assumption is the Hegel is a really good amplifier and has plenty of power, but can't imagine the streamer is world class.
I'd add a high end streamer since you indicate that is where you listen to most of your music. Aurender, Innuous, or Lumin would be great places to start. Find the right one that fits your needs (network player, transport, storage or no storage, DAC or no DAC, CD ripper or no, etc), but I personally would wire it direct with the ethernet port. Others may disagree with that observation.