How to configure Approvals for changes to accounting on fully-paid invoices?

Sometimes we need to correct the accounting on fully-paid payables invoices. And as a small municipal organization, we are unable to rely on security roles, alone, to provide the appropriate Internal Controls. We need Approvals -- or at least something more than a report we run periodically -- but only for these changes to invoices.

For example, an invoice is charged to a particular account when it has been paid. Then sometime later, we discover it should have been charged to a different account -- or to a project. We need to update the Invoice accordingly.

Trouble is, Approval Workflows won't trigger because we're