You'll probably have to edit the model to change it. If you are going to "dig around", doing it in nifskope is probably the best idea if you haven't yet.
This too.
Open the armor in Nifskope. Select the NiTriShape(s) and expand it (them), select BSDismemberSkinInstance and look below in the Block Details. Expand Partitions and see what's written under BodyPart. You're looking for something that says SBP_32_BODY, SBP_34_FOREARMS, SBP_38_CALVES. This is for armor (chest piece).
Then look at the amulet(s) too. Particularly look at the one the armor replaces. Amulets should have SBP_35_AMULET in the Body Part.
Just compare the info in the .nif with with each other then with the data in the CK.
Maybe it's not the fact that the armor replaces the amulet. Maybe the amulet has improper Body Part set in the .nif and the actual model is invisible in-game.