Muting was the first and most important big thing on a six-string for me as well rather getting the high C involved in my playing.
Adam Nitti´s introduced technique is part of mine as well. The floating thumb is one of different keys for a good muting.
In addition to that I´ll support my plucking hand by muting with my fretting hand as well where it´s necessary. It´s mostly the pinkie and ring finger.
So if you get into slapping the muting looks different. It´s depending on which height your bass is located on your body.
Mine rests somewhere in the area between my hip and chest. Therefore I can lay my underarm on the B and E string gently and mute them while thumpin´ and pluckin´. Also here my fretting hand will support the string-muting for example with left palm-hand-muting.
For further fingerplaying it is useful to watch John Patitucci technique too. This is a bit advanced. He used to anchore his pinkie and ring finger of the plucking hand on the B (pinkie) and E string (ring finger) plus his floating thumb for the next strings. He uses the pinkie and the ring finger as a pivot when moving to the higher strings like D, G, and C.
I tried this out and find it became a quiet naturally approach too. Sometimes I used this pivot beginning resting on the E-string and so on. So I apply a different mix of muting techniques in order to what sound I want to get out of my six-string.
And I´m still practising and exploring, it´s never over.
For pick-style muting watch Anthony Jackson what he does when it cames to him he has to play with a pick on a 6-string. It´s much easier, because you can apply the palm-muting of the plucking-hand.