I had had nothing but good weather in 3 prior trips to the Tuamotos (2X in January and one time in April). When I returned in January 2015, I had 5 good weather days in a row and then the odds must have turned on us because we saw three storms in a row over a span of 10 days, the last one with strong enough winds to be called a hurricane (75mph). I am going back this year, but in June, not so much out of weather considerations but more so to try to catch the grouper spawning.
But as the OP hinted, for us who live in colder climes, going to the tropics during our wintertime is our way of escaping the snow and bone-chilling temperatures.
So for my following trip there, it will probably be during North American winter season, and December, I have heard, is mighty good for seeing schooling eagle rays because they come in to mate, and that, in turn, attracts Great Hammerheads, who apparently like to feed on eagle rays. Interestingly enough, I have had better luck seeing Great Hammerheads in Fakarava than in Rangiroa.
As far as certifications, all of the previous comments are spot on. PADI OW and even AOW only gets you CMAS 1 star. You need PADI Rescue Diver to get CMAS 2 Star. Not having it might limit how deep they are willing to take you.