In your use case, in the editor the Property uses a different backing field for serialization and the intention is to access this data directly through a field at runtime to avoid extra check. This means that similarly to the Property you would need to initialize the value at runtime and would not need Serialization of the value. If the attribute [System.NonSerialized] is used against the field it will be present at runtime and accessible and will therefore not produce build errors as the serialization layout will be the same.
In attachment I have modified the code to demonstrate an initialization on Start. Another alternative would be to use ISerializationCallbackReceiver.OnAfterDeserialize to do this initialization at runtime. Unfortunately this will add a couple of bytes to your object at runtime. Though you would need to be cautious that those approach won't work if this code is called from a precompiled library.

Another alternative, is to make the property logic very minimal for runtime.