What happens if the order is edited in Shopify? Do you support that, or is your application the source of truth?
If the order cannot be edited by Shopify admin or an app, storing the fulfillment order and fulfillment order line item ids will give you the info you need. An order edit may invalidate these associations. Does your app already re-process an order in reaction to order edits?
I hope that helps and does not actually makes it worse.