Last thought on AM vs. Airplay. I ripped all my cd's on my laptop years ago, so my 'local' songs are all at the bit rate I ripped them at. Could have 128, could have been 256, may have even been MP3, IDK. But as has been pointed out many times, iTunes match doesn't upload YOUR song if it is in the Apple music library already. It just adds their copy to your online 'Library'. So the Apple version that is 'downloaded' to you HP directly could be a much better quality than the one you ripped on your computer, synced to your phone and are Airplaying to the HP.
Although I guess no one, myself included, actually sync their phones anymore. But hey, it's just a thought.