Reconcile the account to the payment history every month

An account that contradicts what was applied for and certified all year invites the other side to treat the whole thing as newly invented. Keep the running final-account position reconciled to the interim payments as you go, so the closing figure is visibly the sum of what was claimed and certified month on month, adjusted for what was agreed. Arriving already consistent with the job's own payment record, most of it is conceded before the first meeting.