Applying a payment to an invoice before its posted or exported is honestly a need! I hate having to create the payment, add it to a customer profile, then later adding that payment to the invoice before i print it. If i print the invoice for my guys before the job is complete, it shows the whole amount, not just their remaining balance. Then if i forget to apply it to that invoice later, it looks like they are way past due when they arent.
Are you using Progress Billing or is this just a standard invoice? A standard invoice should show all applied payments even if the job isn't completed... I haven't dipped my toe into progress billing yet, but if it's applied to an Invoice on the Project (we do use projects). Then whenever you choose to print the Project Invoice the payment should show as long as it is applied to an Invoice and not just an Estimate/credit on customer's account... if it's only been applied to an Estimate then it won't show until you move it to the Invoice.