I have both issues with my '21 Rebel and the HK system. In Orlando, there's one rock station that boosts their signal for HD radio. When I listen to that station, the speakers sound awesome and my bass is at +6. I don't get much bass response at lower volumes, like at 5 or 6, but you don't want heavy bass when the volume is low for conversation. With nobody in the truck, I run at 12-16 for volume and the HK is awesome.
Now, if I go to any other station, HD or otherwise, I need to turn the volume up and the bass response is minimized, compared to that one HD station that sounds awesome. All radio stations and SXM have the same sound, with some bass at +6, but nothing like the sound I get from that 1 rock station. Not sure why.
When I tune in to the good HD station, it sounds just like every other input for the first 5 seconds or so. Once the HD signal kicks in, the sounds and frequencies are amplified. I wonder if it's the station or the radio signal processing.