IMO IF you have no reason to sell it/trade it currently, then keep it as it is. The main plus you have is the rarity of it being a 6.5 if your pop report is correct (I havent looked). Cant personally see any other advantages of changing its state unless it really bothers you, and we cant help you decide that.
What difference will authentic be over a odd grade when mixed among your higher grades.
Just to add one minor correction quick before my comment, @justmatt just be aware that 6.5 as a grade doesn’t really equate anything special on top of its rarity as a whole. Rarity and grade are different measurements, and while some grades warrant a premium, the grade mark is merely only a reflection of condition rather something overtly special in terms of the card. Also, not many people opt for psa half grades ever, which is typically where bgs comes in to fill that void. Just wanted to add that lol
but! Justmatt I also agree with on keeping it as is if not looking to move it. Im a 9 collector myself, but for something as hard to get as a 1st ed zard, the demand will always be there regardless of grade. But if its too much for your senses to keep, authenticating is a happy medium there to ease the grading illusion 
Hope this helps!
throw it away
thanks for the answers guys , i tried deleting the post but the other responses remained xD sorry about that