How much trouble is it to find a record 3 years old? According to how you have your records set up, can you not go straight to relevant one? It is not like you have to go through every record you have from this date back 3 years. I don't understand that argument. It would seem that you are one to keep records. It would aloso seem you would have know at the time if everything had been paid for, invoice or not. I would look at the record. If your memory is a little hazy, take a look. You may have been invoiced.
No contract? Work order?
Sol may apply here in one way or other. Statue of limitations may even apply.