I'm trying to export using WP All Export from the site, and Importing to the same site bus under a different language.
I have used the WPML addon, but I'm not sure how to link each of the new posts that have been imported to the default language - so they are all showing up as a complete different post.
You have content on your site that is in a secondary language, and you want to essentially duplicate that content to the default language, and you are trying to do that by exporting the secondary language content then importing it as the default language.
Is that correct?
The problem with this workflow is that to connect translations of content when importing posts it is necessary to import all language versions of the posts. The process of connecting posts in a second language to posts in another language depends on those first posts having also been imported using the same technique.
In your case I think you would need to export the existing content, prepare the CSV files for both the existing language and another for the second language, and either delete the existing content from your site before re-importing it, or re-import the existing content and overwrite the existing posts. Once you have imported the posts of one language you can import the second CSV file to connect the posts of another language.