How do I clean up image uploading by removing the additional upload fields?
You can do this. Although it may not be what you exactly want. I'm not going to write all the code for you, but can push you in the right direction:


Make the field accept unlimited values. That will add your "Add another" button, and will only show 1 image upload field initially.
Make a small module which implements hook_form_alter and modify the node_form of the content type which has the image. You need to add an extra validation function. 
Write the validation function to check the number of values supplied in the image field. And set form error if more than 6 images uploaded.