The second argument of withExistingParent is the path to a model file to use as a parent, not a texture. For basic block items, the model normally uses the block model as the parent, rather than specifying individual textures.
I use this helper method in my BlockStateProvider implementation to generate block item models that simply extend the block model. You can see an example of this here.
On a side note, the DeferredRegister instance should always be created in the same class as it's used in; don't put the DeferredRegister and RegistryObject fields in separate classes.