I don't know the wine cooler that you have but it almost sounds like it is a compressor style, that would explain the quick drops and when it kicks off you are over humidifying the space and you get a rebound high. You can also try getting a small bag of spanish cedar shavings to help stabilize...
I went here and had shelves made, I also got a bag of wood shavings to help maintain the RH and I have not had a problem. But I also do not have a cooled unit.
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