So do I understand your payment schedule to be....sometimes it's this way....sometimes it's that way...but it's never the same twice?

Under American contract law payment is due at the time to which the parties agree. Late payment is contract breach. Furthernore, the title abstract remains the property of the abstractor until he/she is paid for the work. If you are using the abstract before you pay for it you may be subject to suit for contract breach or possibly under the doctrine of Conversion of Property.