*Specify* is the best I can think of, but it doesn’t by itself 
capture the change from ambiguity to less ambiguity.

For example, does this make sense grammatically? Assume I can’t 
remove the words, *his statement*.
> "That ship cost me my entire net worth to ride."
> He later specified his statement: "It wasn't a boat.
> It was a *rocket*ship that I paid exorbitant amounts of money to
> ride."

I’ve tried searching for synonyms of *specify* and *clarify*, but
none of them does the trick.

A compound word or phrase would be acceptable.

EDIT: Add original statement: "That ship cost me my entire net worth to ride."