If you are going to have rules like this then you will get arguments, and to be honest, I am afraid you deserve arguments with rules like these!
In most of the world once you have started a board you are always
allowed to finish it. I strongly advise you to follow this in future.
You can always apply pressure in other ways. You can stop people from starting a board within two minyutes of the move being called, apply procedural penalties, or anything else you like.