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nope, creature's owner picks one totem armor and removes it, thereby removing the destruction effect from the creature.

Yeah that sounds right, both totem armour effects trigger and hit the stack but when the first one resolves the destroy effect is canceled by the wording if the creature would be destroyed remove all damage instead. Therefor when the second totem armour effect on the stack resolves the creature is no longer being destroyed so the effect fizzles and the armour is not destroyed.
The controller of the creature decides how to stack the various totem armour triggers so he controls which one is destroyed.