The solution for Safari was very simple, but I do not understand why it was the solution.

Changing this:

setcookie( 'cookiename', '1', time()+1200, '/' );

... to this:

setcookie( 'cookiename', '1', time()+1200, '' );

Using an empty PATH parameter and PHP and JS both recognize the cookie and value.

I would love to know why this is the solution for Safari if anyone can elaborate!

Cheers