You should omit 'the' in the adverbial case if there's no additional context because the verb is ambitransitive.
In: `She woke the latest in the family,' "the latest in the family" acts as the object taken by the transitive verb. Consider:
"Jan is the oldest child. Then there's Mike and Dan."
"Who's the youngest?"
"Daniel is the latest of the children in her family."
"Jan woke Mike, and then she work the latest in the family, Daniel."
Also, as an adverb: 'She woke up the latest in the family':
"Who woke up first?"
"Daniel, then Mike. Everybody was awake but Jan."
"So Jan woke up the latest...?"
"Yes. Jan woke up the latest."
Jan woke latest. - Without 'the', there's no chance latest is an object.
Jan woke, the latest. - The comma creates allusion and a new ambiguity.
So, the sooner is better.
With the be verb, no disambuation is necessary with "the"; however, there is sometimes ambiguity when 'the' is excluded.
Jan is the latest waker. This isn't ambiguous.
Jan is latest waking. There is an ambiguity:
Jan is latest waking. - Jan is latest and is waking now.
Jan is latest waking. - Recently, Jan is the latest at waking.
Jan is latest--waking. - Jan is the latest and is waking now.
Jan is latest-waking. - Recently, Jan is the latest at waking.
However, em dashes are advanced and highly subject to style, and it would be a niche situation in which an em dash would be used in this way (someone is quickly jumping from thought to thought). If we were to take a different situation, this may be a more important disambiguation, though, because an em dash can also be used to define (especially in transcription):
My carrot juice is the best--drunken or stored;
pure, clean, and healthy; tasty, too--if you like juice.
In this way, we capture the words, as they are spoken, with the intended meaning.
If you want to be clear, try this:
- Use "the" for superlatives acting as objects, complements, or subjects.
- Omit "the" for superlatives acting as adverbs.
- Use ", the" to participate with the theme, or to emphasize the superlative.
Additional context allows "the" to be included as part of an adverbial superlative; however, this is largely euphonic. There's no reason to include "the" in non-complement cases.
Additional reading suggests "the" is not omitted with concrete nouns. "Most" usually takes concrete nouns, so it's a good example.
She writes the most books.
When acting upon plurals, 'the' is often omitted.
If you want, make your jumps highest.
But there are no concrete rules. You have to create your own style and go with what you know makes the reader will understand.