Adding past charges a second time to a new invoice can really mess with the accounting. Follow @chipoffblock's guidance and create two items: an new invoice for the new charges and a "Balance Forward" Statement for the old transactions. There are a couple ways to send the Balance Forward Statement:
Go to the Sales Tab and and then the Customer Tab. Find the customer and click the down arrow icon on the list next to their name ( ). Select "Create Statement" and set the date range on the form. Click send and it's off!
Make sure you follow up with the customer :), though they probably get the hint.
If you want to send Balance Forward Statements to multiple customers, you can do a batch action. Click the Plus Action Icon () and select "Statement." You'll be taken to a form screen. Select "Balance Forward" as the statement type and set the date range.
You can also choose to forwardOpen balances or just those that are Overdue.