You have not registered a renderer for your entity. Your attempt at doing so does nothing, because your event handler is never called, because @EventBusSubscriber registers the Class to the event bus, but your method is not static.
Any dynamic item data must be stored in the ItemStack. There is only one instance of your Item class.
Use ItemStack#getOrCreateTagElement with your ModID to get a CompoundTag. You can store whatever data you want in this tag.