In case anyone ever stumbles across this:

1. I wish you the best of luck.
2. The solution was to use an IContentApiModelFilter instead and append the property just before the content is being sent to the client.

The solution looks like this:

    [ServiceConfiguration(typeof(IContentApiModelFilter), Lifecycle = ServiceInstanceScope.Singleton)]
    public class CustomContentApiModelFilter : ContentApiModelFilter<ContentApiModel>
    {
        private readonly IContentLoader contentLoader;
        private readonly IContentTypeRepository contentTypeRepository;
        private const string CONTENT_TYPE_GUID = "ContentTypeGuid";

        public CustomContentApiModelFilter(IContentLoader contentLoader, IContentTypeRepository contentTypeRepository)
        {
            this.contentLoader = contentLoader;
            this.contentTypeRepository = contentTypeRepository;
        }

        public override void Filter(ContentApiModel contentApiModel, ConverterContext converterContext)
        {
            // apply any filtering as needed... etc

            contentApiModel.Properties[CONTENT_TYPE_GUID] = Guid.Empty.ToString("N");
            if (contentApiModel.ContentLink.Id != null && contentApiModel.ContentLink.Id.HasValue)
            {
                var content = contentLoader.Get<IContent>(new ContentReference(contentApiModel.ContentLink.Id.Value));
                var contentType = content.ContentTypeID;
                var type = contentTypeRepository.Load(contentType);

                if (type != null && type.GUID != Guid.Empty)
                {
                    contentApiModel.Properties[CONTENT_TYPE_GUID] = type.GUID.ToString("N");
                }
            }
        }
    }