Can one make a UProperty readonly in a subclass?

Say I have a custom component class Container with a UProperty numberOfItems on it. This property is EditAnywhere and BlueprintReadWrite.
Now I want to make a subclass of Container called DVDCase, which should really only be able to hold one item. Ideally for DVDCase I would like to set numberOfItems to 1 from code and make it VisibleAnywhere and BlueprintReadOnly instead of EditAnywhere and BlueprintReadWrite.

Is this possible? And if not, how much trouble would I be getting myself into if I were to try to make it possible? And if too much, what other ways are there to keep someone from changing the numberOfItems of my DVDCase somewhere in the editor?