I use a movable anchor relocating the thumb on the pickup, E and A, I don't usually anchor on an adjacent string, I find that too close for most things. I leave the thumb on the E predominantly for playing over the E, A and D strings, then move the thumb up to the A string for the A, D and G strings, using the top surface of the thumb to mute the E while the bottom mutes the A.
Muting adjacently is something I use on flamenco technique, but I find in too curled and close for standard stuff.
If I locate on the E, I stay there for whatever I'm playing on the E, A, D until it's time to relocate, which in the middle of quick runs, has to be quick. I've always found the attack of floating thumb a little bit light for my tastes, I prefer a movable anchor.