What’s the Simplest Way to Override/Rewrite the %category% Permalink Structure Tag?

Yes, the post_link_category hook is indeed what you would use to filter the %category% replacement value in the permalink.

And here’s an example with prominent_cat being the meta key and the value being the category name (e.g. Pizza Hut), where I’m using get_term_by() to get the category object/data:

add_filter( 'post_link_category', 'my_post_link_category', 10, 3 );
function my_post_link_category( $cat, $cats, $post ) {
    $prominent_category = get_post_meta( $post->ID, 'prominent_cat', true );
    if ( $term = get_term_by( 'name', $prominent_category, 'category' ) ) {
        $cat = $term;
    }

    return $cat;
}

If the meta value is a term/category ID, then you can simply use get_term() to get the category data:

add_filter( 'post_link_category', 'my_post_link_category', 10, 3 );
function my_post_link_category( $cat, $cats, $post ) {
    $prominent_category = get_post_meta( $post->ID, 'prominent_cat', true );
    if ( $prominent_category && term_exists( (int) $prominent_category ) ) {
        $cat = get_term( $prominent_category );
    }

    return $cat;
}