I realized I should do a minimum code example, and EnsureUmbracoContext() worked correctly when I did that. I've narrowed down the issue to some sort of dependency injection weirdness; it wasn't injecting the dependencies on my class because it couldn't find one of them (and was failing silently because I had an empty constructor available). Once I removed the other dependencies and constructors, it worked fine.

So if you have this same issue, try injecting ONLY IUmbracoContextFactory, and make sure you only have one constructor. If that still doesn't work, try it in a separate minimum class, something like the one below.

using Umbraco.Cms.Core.Web;

namespace MyProject.Classes
{
    public class HangfireTest
    {
        private readonly IUmbracoContextFactory _umbracoContextFactory;

        public HangfireTest(IUmbracoContextFactory umbracoContextFactory)
        {
            _umbracoContextFactory = umbracoContextFactory;
        }

        public void Run()
        {
            var cref = _umbracoContextFactory.EnsureUmbracoContext();

            using (var ctx = cref.UmbracoContext)
            {
                var contentCache = ctx.Content;

                if (contentCache != null)
                {
                    var root = contentCache.GetAtRoot();
                    var asdfasdf = root.FirstOrDefault();

                    var homepage = contentCache.GetById(1234);
                }
            }
        }
    }
}

is working on a reply...