Connect Xero once. From then on every approved timesheet arrives as a draft sales invoice for the client and a draft bill for the contractor's self-bill, with VAT codes and PO numbers set. When the client pays, Xero tells Templio.
Templio does the re-keying, not the authorising. Your bookkeeper still approves and sends from Xero, with the numbers already in place.
Xero notifies Templio when an invoice changes, and Templio re-reads it. An invoice is only marked paid once Xero says so, so your overdue list stays honest.
Timesheets in. Approvals done. Both invoices waiting in Xero. Insurance tracked. Margins in view. What's left is the part of the job that makes money.