The traditional monologue, as used in TOS, TAS, TNG, Strange New Worlds, as well as the endings of Enterprise and several movies, can be taken as a sort of overall mission statement for the Enterprise, possibly even one that takes place in-universe.
If the other series-- Deep Space Nine, Voyager, Discovery, Picard, Lower Decks, and Prodigy-- had similar mission statements, how might you phrase them?
Have Boimler give the intro, occasionally interrupted by Mariner piping in with another part, or helping him complete the monologue when he forgets parts? That way, it keeps to the spirit of the monologue, but also includes Mariner, and the kind of comedic levity that is tries to bring the show.
They basically did that with Boimler doing his own log about second contact, back in the first season.