In Part I, I outlined a major scale exercise that uses the entire fretboard. The first method isolates a single key and repeats in all 12 keys. The second, trickier method continually changes keys with every position change.
Part II of this exercise is simple to understand, but a serious mental workout to execute. I use either method from Part I, but stick to two strings at a time. This forces me to visualize complete scale patterns while only playing a few notes from each one. And it gets me really familiar with every possible connection between the five CAGED major scale shapes.
So far, I've only tried this with pairs of adjacent strings. That challenges me enough (I still can't do it without pauses) that I don't need to skip strings yet, but that's the next step. I'm already seeing progress in my jazz improv over tunes with frequent key changes. I can find the new keys faster, and I'm more comfortable moving around the neck. Once I master major scales in this manner, I'll move to pentatonics, melodic minor, harmonic minor, etc.