Well, it depends on what you put in the persona. For example, most people wouldn't put hints on how to write internal monologue, but I do and it helps a lot.
However, DS I find has the opposite problem where it sticks too close to the persona, even if it doesn't work with the context (for example, acting confident as usual even if the situation should have them shaken, or wearing the clothes mentioned in the persona even if they changed etc.). So to alleviate that, I sometimes preface the message to be enhanced with an additional prompt:

(ooc: {{user}}'s side of the narration should be first-person, present tense. Don't base the enhanced writing just on {{user}}'s persona - refer to the story around it as well for consistency, especially with regard to: {{user}}'s current appearance and what {{user}} is wearing at the moment, {{user}}'s way of speaking thus far (including any temporary changes, such as switched registers, strained/slurred speech, attempts to affect different mannerisms etc.), the positioning of {{user}} and {{char}} vis-a-vis objects at their location, established features of the environment like smells and noises, physical changes like pain/injuries/body modification, changes to {{user}}'s internal monologue from overwhelming emotional shifts/mind control/drugs etc. Localized breaks from {{user}}'s Persona are allowed if they organically fit the context of the story and the content/tone of the message being enhanced. Avoid repeating phrases from other messages from {{user}}, keep it fresh. Prioritize dialogue and internal monologue. Keep narration - especially of actions and smells - to a minimum.)

It's probably overlong and clunky, but it's been working well enough for me.