How to stabilize soft nougat?
In my own practice, I just cook the sugar to a higher temperature in order to make a nougat firm enough to not spread.  

However, I have recipes suggesting the use of rice paper, and have eaten store-bought nougat that used rice paper on one or two sides of the nougat to hold it together (and minimize sticky fingers for the people eating it.)  I can vouch for rice paper tasting just fine with the rest of the nougat.