Drupal 7 + Solr - Importing feeds after website restore leads to 1062 Error
It turned out it was the Solr module itself. I'm not sure why it wasn't clearly it's index completely, but after disabling and actually removing the module, then reimporting, everything worked. 

So if you're having this kind of trouble importing content, and you have the Search API Solr module active, first disable and then remove it so that you have a clean slate on that end. Then you can reimport the content, then later re-add the Solr module and reindex your content.