I'd use 1/16th in birch.
My thinking is that end grain is the issue and the water absorption from teeth holes is too small to be a factor as long as you have a good primer- color coat adhesion.
I think the hook hole is the biggest source of water intrusion and I prime them to seal them further. I don't think the through hole is a big worry since wood absorbs water from end grain, not so much from side grain (wood is like a bundle of miniature straws.....water/sealer goes in the ends easily but not through the sides of the wood tubules)
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