It's not the battery (per se) that can be the source of noise, it's the charging system on the positive side of the battery. Some people say it's fine to connect ground directly to the battery, most got away from that practice long ago. I have never seen a mobile amp manufacturer recommend it - mostly because it can couple noise from the charging system. Remember the days of engine whine?
There are 2 ground lugs on the frame. The electrical diagnostic manual refers to the right lug as "clean ground" and the left lug as "dirty ground". Sensitive electrical devices on the bike are tied to the right side lug (ECU, sensors, etc). Other devices (lights for example) are tied to the left ground lug.
My amps are "powered" all the time, because (as you stated) there is no normal "remote on" from the H/K. I don't get any "pop" when I turn the radio on, nor do I get any noise from the amp(s) when the radio is off. As for my gains, I don't remember where they are set. I dialed them in based on sound quality and didn't worry about how much or how little the gain was adjusted. If I had to guess, I am probably at 25% or so. Front amp gains are set different than the rear amp due to different performance specs of the speakers.
Remember, gain adjustment on an amp doesn't adjust an amplifiers output - it adjusts the sensitivity level of the amps input. Dialing in the gains is usually a balancing act of providing maximum output power without introducing any additional distortion by the amplifier itself.
I'm glad you're happy with your project. If it were me, I would move the ground from the battery post and land it on the "clean" lug on the right side of the frame

. But that's just me ... as long as you're happy with the install that's all that is important.