I'm no accountant by any means, but I think there's more to it than just distributing receivables across invoices. To suggest applying 300 and marking #2 and #3 as paid, with the balance being applied to #1 probably wouldn't be advisable. If you can't coerce them into telling you which invoice(s) to apply the payments to, I can only envision applying the payments to the outstanding account balance. To do otherwise and mark #2 and #3 as paid makes no sense to me since the PO or job associated with either of them could still be open. Rather than make this your problem, perhaps you should insist on having them allocate the payments, else use your own discretion based on your knowledge of the business, to decide if you can close out an invoice or not.
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.