Your sentence is much better off as you started, though I would personally prefer not to separate the subject from the verb by too many words:
David, using a metaphor of Saul's, said...
Using a metaphor of Saul's, David said...
This double genitive here is very useful to avoid ambiguity. Although the idiomatic phrase is metaphor for something, many do use metaphor of in this sense. Even Wikipedia does:
Whitman's O Captain! My Captain! uses the extended metaphor of Abraham Lincoln as the captain of the 'ship' that is the United States of America.
So if you say, using a metaphor of Saul, those who are used to saying metaphor of might mistake it as meaning a metaphor, an image, a symbol for Saul, and not a metaphor that belonged to Saul.
The double possessive, usually using both of and 's to demonstrate possession, is grammatical. While it is sometimes unnecessary, it can be helpful for differentiating when the possessive (or genitive) case is about association or ownership, such as in
a picture of my friend
a picture of my friend's.
This kind of construction, known as the double possessive, or double genitive, dates back to Chaucer's time, and mostly gets used without being remarked upon by native speakers. There are, however, people who will tell you to avoid it.
It's true, if there is no ambiguity, the double possessive is definitely redundant. BUT:
The possessive, or genitive, case isn't just about possession; it can
also show that someone or something controls or is associated with
someone or something else. The double possessive, or double genitive,
serves to separate the possessive genitive from other functions of the
genitive. "A dream of Mabel" can demonstrate the genitive of
association [a dream someone had of Mabel], but "a dream of Mabel's" ensures that it's the genitive of possession at work [a dream Mabel herself had].
As a final addition, not so relevant to your question, I will quote a detail that M-W draws attention to in a way that manages to put a smile on your face while at the same time pointing once again to what I might call with admiration the indocility of this fascinating language to fixed grammar rules:
Showing possession with of is normally used when it is a thing that has possession, rather than a person or animal having possession. The double possessive/double genitive, however, throws that out the window. We can say "a dream of Mabel's," but we cannot say *"the winner of the contest's." It turns out that English only lets people and animals be doubly possessive, and insists that they use of to do so. Don't blame us. We're only the messenger.