All told, after decades of research, it seems that Efron-Hinkley holds up -- observed information dominates estimated expected information for finite-sample MLE inference. It's both easier to calculate and more accurate. Let me know if you disagree.
[Efron, B. and Hinkley, D.V. (1978), "Assessing the Accuracy of the Maximum Likelihood Estimator: Observed Versus Expected Fisher Information", Biometrika, 65, 457–487.]