Hi Fi
In my opinion I don’t believe there is a limit on a private treaty and why would you want to incur costs again in going through the whole process for the sale of the property again the following year.
Having satisfied all the conditions of 713 I would continue to try and sell the property by private treaty and when/if you find a purchaser they will apply for a 603 which will let them know all outstanding rates and charges on the property if further rates and charges have been levied.
It might worth getting a legal opinion.
Robert