What is your definition of "still"?
At rest relative to your body, and hence moving with you, or at rest relative to the earth so you can adjust your body?
This is not trivial. Based on your pics I would guess you are asking about the former. With a strap there is really no way to do this AND have your hands free to move around. Classical guitarists don't stand, for example. And I recall that Alex Lifeson from Rush would have his acoustics mounted to a stand on the stage. Of course this was mainly for the song Broons Bane / Trees where the into was classical and the electric part came with no break, hence the need to move quick and keep his electric on his body.
Personally, I'd sit. Especially is I'm playing something intricate on an acoustic. One option is to hold the body with the forearm of your picking hand (but that then restricts the right hand form some gymnastics). If you're playing folk style music and all you're doing is strumming open position chords you really use the "left" hand to hold the ax in place (NOT recommended for any instrument). Other posts have mentioned trying non-slip material, this will work to an extent but realize that there is no such thing as the "slip" from a physics point of view is a relationship between the two materials in contact. So try wearing different shirts, jackets with your existing strap first to see how that goes. Another answer suggested trying different geometries of strap and this is reasonable. You need to make sure that somehow the center of mass of the guitar is supported not only from falling but from rotating about your neck. I'd try and find the CoM by balancing it (without dropping it) and using that to guide how you rig up the strap. It might not be easy but there has to be a way to do it and you may need to adjust your playing style to accommodate the way the ax is positioned.