I was thinking about this earlier and I realised that if you want to break out of patterns, here's a thought:

Continue with the cycle of fifths (or fourths), but insist that you never move to an adjacent string.

I used to practice major chords around this cycle using CAGED shapes, which becomes very predictable. But if, instead, you insist that the root note must skip a string each time, you get:

C (root on E string)

G (root on D string)

D (root B)

A (root A)

E (root G)

which is a lot more interesting.