Trigger the 'add more' button with javascript, to add a set amount of field values
I had the very similar problem, but with a group of fields that all needed to be added in sync. Using setTimeout to trigger is problematic because of the guess work involved.

One of the ways to do this is to use the ajaxSuccess event to chain a list of requests. After searching for a solution to my problem, I ended up creating a small plugin called group-add-more. This can work with both Drupal 6 as well as 7.