If it really is true that you hit the adjacent string when you try to switch strings, try making small adjustments to how your arm and/or wrist is positioned to try to get the picking motion off of parallel to the plane of the strings.
But the direction of movement of the pick doesn’t have to be drastically off-parallel in order for escape to happen. It only needs to be just far enough off parallel for strokes in one direction to escape the plane of the strings (of course some approaches, like the Gypsy USX approach, employ an angle that gives a surplus of clearance on the escape strokes).
If you’re interested in a David Grier type vocabulary, pronating your arm a little to try to get the essential motion you have now shifted slightly so it becomes more of a DSX motion could be helpful. Personally, I’ve found that an approach like your example 2 or example 4 has been useful to my experiments with DSX, because the contact with the ring finger or pinky against the body can help regulate your hand position, which may help you discover a setup that gets the pick to move along the line that you want. Another crude way to think about this is to consciously let the side of your thumb brush the lower pitch strings on upstrokes as you figure out a feel for the picking motion. Don’t overdo that, or you could give yourself a blister on your thumb, but some sparse experimenting at that extreme could help you get a feel for a motion/setup that will help you work your way into DSX without the thumb friction.