great question. it's a bit hard for me to specifically comment without seeing your hands, but for applications like you have described, it's better to leave the thumb in a static position for both octaves. for me personally, i only move the thumb/anchor if i'm having to reach beyond a 2 adjacent string-width. that way my hand position still stays relatively consistent and i'm only having to momentarily 'reach' to grab the octave or higher notes. in instances like you have described, it's best to look at your hands and analyze what is the most efficient solution. the basic movable anchor method is a great foundational approach; however it has to be tweaked to accommodate particular playing scenarios. as long as you are efficiently muting and managing reasonable (and relaxed) hand positions, you are on the right track. hope that helps!
AdamNitti.com - AdamNittiMusicEducation.com