How to integrate order management with 3rd party billing system

Summary:

We have a third party billing application which calculates tax and distribution lines for each sales order. Our requirement is that the OM data is passed to 3rd party billing system, updated and passed back to Fusion before the AR invoice is created. As such:

SO Fulfilled (Awaiting Billing) > Send to 3rd party > 3rd party sends back updated invoice lines > AR invoice created in Fusion > SO closed

Content (please ensure you mask any confidential information):

we have already explored REST API's but they only allow a very limited amount of updates and only at header level.

We've also explored FBDI but this only allows 'CREATE' transactions. This breaks the link between OM and AR and impacts SLA too much.