how about not having a big fat "PLACE AWARDED" box on the cover page? they could even go so far as to print on that cover page "Placement will be announced at a later time, once all judging is complete". seems simple to me.
The "place awarded" thing is boilerplate on the BJCP coversheets that accompanies all scoresheets. It has nothing to do with the AHA or NHC. In a regular BJCP competition those are filled out by the head judge at each table.