Currently it's possible to read the custom categories attached to a product via the API, but not change them.   For that, we have to export a CSV and upload via the import system, which is cumbersome.  Please add an API endpoint to enable this.  
For example, to add a ContentID to a product
<UpdateItem>
<Item>
<SKU>HMT41GU6BFR8A-PBN0</SKU>
<RelatedContents>
��<RelatedContent>
����<ContentID>148675</ContentID>���
����</RelatedContent>
����</RelatedContents>
</Item>
</UpdateItem>
or delete it....
<UpdateItem>
<Item>
<SKU>HMT41GU6BFR8A-PBN0</SKU>
<RelatedContents>
��<RelatedContent>
����<ContentID>148675</ContentID>���  
    <Delete>True</Delete>
����</RelatedContent>
����</RelatedContents>
</Item>
</UpdateItem>