It could be made so that completing the current GL combos activates the fist buffs instead - once GL becomes a trait. They could even make use of the MP bar to portray the channeling of Aether into their fists.
Demolish could activate Fists of Fire. When used, FoF could increase Direct & Crit Hit rates by a lot while draining MP with each GCD use in lieu of a buff timer. Six-Sided Star could maintain its current position as a GCD time extender to 5s with a high potency but cost no MP during FoF and be given a longer-than-GCD personal cooldown (like Drill/Air Anchor).
Snap Punch could activate Fists of Wind. When used, FoW could increase movement speed, recover MP and activate Tornado Kick which has a short cooldown, is oGCD, and restores a set amount of MP with every usage.
This would allow MNK to retain its current combos while adding in some BLM-like back and forth - the balance of which makes sense for a monk, kind of like the Taoist Yin and Yang. It would feel a little busier with switching on the fists between GCDs.
Rockbreaker could activate Fists of Earth. When used, FoE could
decrease damage taken and reduce Enlightenment's Chakra cost to 3 charges. It would be a buff beneficial to AoE situations and focus on the meditation side of Monk.
Riddles could be altered so that it is one button: Riddle. In FoF it becomes Riddle of Fire and increases one weaponskill's potency by a lot. In FoW it becomes Riddle of Wind and allows you to ignore positionals for a short while. In FoE it becomes Riddle of Earth and grants you some HP shielding like Stoneskin. Each time you use a Fist, Riddle's recast is reset so that you have one use per Fist. There could be a trait that gives Riddle 2 charges at higher levels.
Anatman's name meaning actually is the opposite of its effect - anatman buddhism basically is the idea that there is no one permanent unchanging soul but rather the soul is made up of 5 ever-changing essences. Perhaps it could be reworked to function with Chakra similarly to Improvisation or be merged with Brotherhood somehow for a new effect.
In the end we'd see a better (or more bolstered) representation of "The Three Teachings" of Buddhism (chakras), Taoism (balance) and Confucianism (riddles) in MNK than we have currently.