English to German Law/Patents Law: Contract(s)

It's a normal contract and I am adding the previous and next paragraph for reference.

"If the Parties are unable to agree on an independent auditor within 14 (fourteen) days, the independent auditor shall be appointed at the request of either Party by the Institute of Auditors in Düsseldorf.

The then appointed independent auditor shall determine the items in dispute by way of an expert opinion; in doing so, the independent auditor must remain within the range of the positions taken by the Parties.

The corresponding accounts issued by the independent auditor shall become final and binding as soon as the Parties have been notified by the independent auditor."

So far I have come up with "sich innerhalb der von den Parteien vertretenen Positionen bewegen", but am not quite sure if it conveys the whole idea.