[eluser]pickupman[/eluser]
I am doing this the other way around but the same method still applies. First you will want to exclude the CI subfolder in your WP(root) .htaccess file. You can configure CI to use the WP database, you just probably want to make sure you namespace your tables. The way of using your WP theme is to use curl/file_get_contents of your home page, and use a regular expression for the body tag. Cache the result to a file (check out the link in my sig). You could create a library to do this, and use Phil's Cache library to save the page. Then replace the html content inside the body tags with your CI views.
As your front page changes (sidebar, header, etc), your CI will stay in sync. You can update your cache on a expiration that would be reasonable to match the freshness of the content/home page.