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The way this should be accomplished is to start off the auto order items auto order steps with a "pause" step and then set the delay until a future date. All new orders placed will pause rebilling until that date. As you ship for that month, just edit the item and set a new pause date.
How do I go about making changes to a specific customers' auto order only? (change items, billing amount, etc.)?
To affect the auto order if a specific customer, you'll make the changes within the "auto order" record. (Changes for all customers with active auto order for an item, you'll need edit the auto order steps within the "auto order" tab, in item editor.
Related Documentation
Auto Order Processing Configuration screen (must be logged in to access)
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