How do You Create a Read-Only Dependency Property?

It's easy, actually (via RegisterReadOnly):

public class OwnerClass : DependencyObject // or DependencyObject inheritor
{
    private static readonly DependencyPropertyKey ReadOnlyPropPropertyKey
        = DependencyProperty.RegisterReadOnly(
            nameof(ReadOnlyProp),
            typeof(int), typeof(OwnerClass),
            new FrameworkPropertyMetadata(default(int),
                FrameworkPropertyMetadataOptions.None));

    public static readonly DependencyProperty ReadOnlyPropProperty
        = ReadOnlyPropPropertyKey.DependencyProperty;

    public int ReadOnlyProp
    {
        get { return (int)GetValue(ReadOnlyPropProperty); }
        protected set { SetValue(ReadOnlyPropPropertyKey, value); }
    }

    //your other code here ...
}

You use the key only when you set the value in private/protected/internal code. Due to the protected ReadOnlyProp setter, this is transparent to you.