Importing New Posts from Live Site into Local Dev Site

Have you considered to use REST API to bridge the two environments?

Basically you need to hit the posts endpoint https://example.com/wp-json/wp/v2/posts using the after argument that permit to limit response to posts published after a given ISO8601 compliant date.

With the response you can insert new posts and sync the two installation.

More detail about the endpoint and the arguments can be found here https://developer.wordpress.org/rest-api/reference/posts/

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