""The doll dances!" Marcus exclaims."
Translation:"Pupa saltat!" Marcus exclamat.
Classical Latin requires oratio obliqua, such as Marcus exclamat pupam saltare. Mediaeval can get by with Marcus exclamat quod pupa saltat. What we are required to do just isn’t Latin, so I wouldn’t worry too much which order the words come in. Your version is just as “good” as any other in the circumstances.
EDIT: Please ignore!
But Classical Latin includes direct quotations of the speaker, when accompanied by a word like inquit, ait, or (here) exclamat. They didn't have the punctuation device called 'quotation marks,' but they did manage to embed "said Marcus" (or the like) in the middle, typically, of his quoted words.
I really should start checking before commenting. exclamat actually comes quite often before what is said in oratio recta, but usually with an adverb or some other phrase, unlike ait and inquit (etc.) which as you say come after the beginning of what is said in oratio recta.