I have tried to create proxy properties that display the VisibleInMenu property like so.

  public virtual bool ShowInNavigation {
            get {
                var show = this.GetPropertyValue(p => p.VisibleInMenu);
                return show;
            }
            set { this.SetPropertyValue(p => p.VisibleInMenu, value); }
        }

But they all show "null" even though value is true or false.

I guess there should be a simpler solution but this was my solution. 

I can actually find properties that randomly dissapear now.

I add them manually here:

    [ServiceConfiguration(typeof(IContentModelMapper), Lifecycle = ServiceInstanceScope.Singleton)]
    public class CustomContentModelMapper : DefaultContentConverter
    {

        public CustomContentModelMapper(IContentTypeRepository contentTypeRepository,
                                ReflectionService reflectionService,
                                IContentModelReferenceConverter contentModelService,
                                IContentVersionRepository contentVersionRepository,
                                ContentLoaderService contentLoaderService,
                                UrlResolverService urlResolverService,
                                ContentApiConfiguration apiConfig,
                                IPropertyConverterResolver propertyConverterResolver)
                            : base(contentTypeRepository,
                                  reflectionService,
                                  contentModelService,
                                  contentVersionRepository,
                                  contentLoaderService,
                                  urlResolverService,
                                  apiConfig,
                                  propertyConverterResolver)
        {
        }

        public override int Order => 200;

        protected override ContentApiModel CreateDefaultModel(IContent content)
        {
            var baseModel = base.CreateDefaultModel(content);
            if (content is SitePageData sp)
            {
                base.AddToPropertyMap(baseModel.Properties, nameof(sp.MetaKeywords), new StringPropertyModel(new PropertyString(string.Join(", ", sp.MetaKeywords))));
                base.AddToPropertyMap(baseModel.Properties, nameof(sp.VisibleInMenu), new BooleanPropertyModel(new PropertyBoolean(sp.VisibleInMenu)));
            }
            return baseModel;
        }
}