Exporting a site doesn’t remove it from the server or empty the database tables. It just exports the site into an xml or similar file. I’m not saying what mercime suggests won’t work for you but it did not work for me.
My problem is similar to yours but not exactly the same. I get all posts imported (339) going back to 2007. My problem is I only get 755 of over 1500 comments attached to those posts so I only have comments going back to around November of 2009.