We had a very similar scenario with a custom image field inheriting from Sitecore Image field. Tried all of the above, without any success whatsoever getting the references added to link database.
The way we solved it was to use the namespace for the field we inherit from when registering the field type within <fieldTypes>:
<fieldType name="Our Custom Image" type="Sitecore.Data.Fields.ImageField,Sitecore.Kernel" />
All of our custom overrides and UI changes for our custom image still function when working within content and experience editor, so I'm guessing that the field registration in node fieldTypes relates only to link database.
Hope this helps.
Cheers, Christopher