I'm not certain I understand what you're actually struggling with, but here goes.
You know 'the CAGED system' and use it to play chord shapes, arpeggios and pent. scales, but only in key C. For me, the CAGE(D) system works for chord shapes only. I must have learned everything else in other ways. Its use in chord shapes is that there are 5 basic shapes on ...
It's just a game of maths as far as I'm concerned. For example, take the C major triad - C E G - and think about all the possible places where you can play those notes.
Looking at C.
E string - 8th/20th fret
A string - 3/15
D string - 10/22
G string - 5/17
B string - 1/13
You can figure out E and G yourself...
An inversion is just playing the same chord from ...