How to Mass Update Bill To Site for Lease Contracts

I have a customer which had a bill to site and dozens of  lease contracts booked using the same Bill TO site. Now customer has a new bill to site and wants all billing to be sent to this new bill to site.

I tried adding a new Bill To site and inactivate the old one, but still all the invoice generated after the change still goto same Bill TO.

Is there a way to handle this without triggering any accounting events (ie rebooking).