yes, that does seem to be the case in that the moon effects the game in many aspects. it could also be that people are looking for a reason why things stop working the way we feel it should. it may be that we just ran into a streak of bad luck.
i'm just speaking for myself, but i've been crafting for over a year. i grinded all my crafts to 50 and didn't use the massive sp boosts from leves and free sp off ifrit. i noticed a drastic difference between the hq rates for myself during half to full. i have a friend that is the opposite and you could tell a major difference in theirs half to new. those differences didn't seem to matter if working on magic craftsmanship synths or regular craftsmanship. it's strange that i have better luck farming mats during the half to full as well.
that's why i say it could be either it's based per person's choices during character creation or it may just be us looking for something that isn't there and it's just a random case of luck. i can't say which is correct, but it's answers i would love to get.