Do you use EQ? I’ve never heard the HD 650, but I do have the HD 600 and feel very similarly about it. Other than my powered monitors, it’s got probably the most natural sounding tonal balance I’ve heard (in the midrange and up) but the bass isn’t great and their grain really stands out in comparison to my DT 1990s and LCD2Cs. It’s not as bad as I remember the grain in my HD 598s, but still very noticeable and not pleasing.
I’ve found that tonal balance on something like my DT 1990s is something I can largely correct with EQ without suffering adverse effects, so that’s basically what I do. Have you played with EQ much to see if you can make your more technically sound headphones achieve an HD 650 tonality?