Rob,
For the other extension you were using, you would have had to authenticate the LinkedIn app at some point with your LinkedIn. Then, the extension you were using sounds like it simply asked for the user's email address to create the account locally. That's what I was recommending with the changes we can help with above... hide all the other fields on the Login or Register page, except email (since we need that).
For editing all the text, it's pretty easy. All of that should be contained in the JLinked language file at /languages/en_GB/en_GB.com_jlinked.ini. If you want to hide the left hand side of the form, we can even help with that
Let me know if that helps explain or not. If you need more info though, we're here to help!
Alex