According to the storyline, there are several Links. Ganon is always Ganon, and good is able to simply stall him for a while by imprisioning him. When he releases himself it might take years, more then a normal human lifespan. That's why everytime Ganon returns, Link and Zelda reincarnate. So far, there is something like 6 Links already, along with 6 Zeldas. It's completely possible that this incarnation is right-handed, since it's a different person.
Reboot storyline. why always trying to connect all those story. i see them as variation of a legend maybe.
Miyamoto has said that there is a master document that links all the storylines together. Also, Aonuma said that he plans on revealing the connecting points of the storyline in the future. So I guess that when they made the first storyline zelda (A Link to the Past) they wrote a document that acted as a pseudostoryline.
and then start the inconsistancy.