It could be tied to per-rest. Similar to the fighters' weapon mastery in OneDnD, switching stances could be tied to a long or short rest instead. Just call it something else, like katas. (Yeah, yeah, they are trying to move the monk away from the strictly Eastern roots, but they could give this as a flavor option.) You drill one of the katas in the morning and then you can use the basic ability associated with it for free:

• Kata of the Wildfire: aggressive stance,
• Kata of the Mountain: defensive stance,
• Kata of the Zephyr: mobile stance.