To The Left, To the Left - SOLUTION

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First observation: There are are eight Down entries whose clues are starred, each of whose answers starts with the name of a Hebrew letter:

• 3-Down: (Mercury, by another name) = HErmes (ה)
• 6-Down: (Michelangelo's implement) = NUNchaku (נ) 
• 9-Down: (Roof part) = SHINgle (שׁ) 
• 12-Down: (One leaving the office) = LAME Duck (ל) 
• 36-Down: (WWII fighter planes) = HEllcats (ה) 
• 40-Down: (2012 Nicki Minaj song) = VAVavoom (ו) 
• 43-Down: (Part of picking a candidate to win (there's an alternate answer)) = BETting (ב) (more on this in a moment) 
• 52-Down: (Suggestively named mountain range) = TETons (ט) 

(There are lots of common ways to spell He / Hei / Hey; I went with the one that's on Wikipedia.)

As suggested by the Beyoncé lyric in the title of the puzzle ("To The Left, To The Left"), you should read these from right to left (since it's Hebrew), first across the top and then across the bottom: in order, we have Lamed, Shin, Nun, He, Tet, Vav, Bet, He. These spell out L'SHANAH TOVAH (לשׁנה טובה), which as requested is a seasonal greeting (Happy New Year), and thus the meta answer.

But wait, what's with 43-Down? Some people think of Bet (בּ) and Vet (ב) as separate letters, perhaps thanks to Debbie Friedman, although that's really not correct; they're just different forms of the letter Bet, written with or without a dagesh. Nevertheless, to avoid complaints from the peanut gallery, the clue has the alternate answer VETTING, which is also part of picking a candidate to win. (Of course, VETTING doesn't work with the Across entry - I couldn't think of any other B/V word pairs that would fit - which reflects that BETTING is really the right answer in terms of Hebrew grammar.)