Hi Todd,
First up, i am surprised cleardb won’t allow you to upgrade the plan ?? that’s…odd.
Second, you can use any of back up plugins and back up your entire site to an online storage such as dropbox. Once the back up I done, you can restore the backup after creating a new WordPress site with the cleardb plan. That’s what I would do.
About the connection string, I am afraid I don’t know anything about that. I am not much of a database developer.