flat right hand notes

[TNFlute]

I just got a new piccolo and mostly love it. I have found that the left hand notes are as a whole flatter than the right hand notes. And the top G is terribly flat. The top G on my previous piccolo was flat so I am used to an alternate fingering but can't always get to it in fast passages. Should I move the headjoint cork in toward keys slightly? I am at A440 when I pull out about 3 mm. (Thickness of 3 dimes) It is an A 442 piccolo. Any ideas out there? I am well aware that there are no perfect scales on the piccolo. I have played many brands and practice piccolo a lot to get accustomed to the alternate fingerings and any lipping.