I have waited a long time to post this but I can no longer hide my conclusion that there really is a difference in the sound between the different gain settings. It is almost as if (or may actually be that) the Pico Power is delivering more power in high gain mode. My Heaven VI is very sensitive to power, ramping up in the bass and mids as power increases. It is one of the reasons that I love the Pico Power so much with it. I am finding that I get more prominent bass with noticeably increased mid-bass slam on high gain by comparison with low gain. (I am not sure what to make of mid gain; I am actually not sure why this setting even exists.)
I thought that it might be placebo but listening today to Janis Joplin's Greatest Hits, the difference was impossible to ignore. (I was doing careful channel matching as much as possible when switching back and forth.)
The volume pot on my Pico Slim has excellent channel tracking right down to the bottom and I am using it on high gain now with IEMs. I don't get a lot of play adjusting volume - low gain is better for that - but with the stiff but still smooth volume control, it is fine.
To be sure the Pico Power sounds just great on low gain. But for that little extra bass pop with the Heaven VI, it is high gain for me.
With other headphones it may not be as noticeable. (I do feel that it is still there with Flat4 Kaede but it is less obvious.) I wonder if others have experienced the same thing?