See the webpage
The Hubble Constant, maintained by John Huchra, at the
Harvard-Smisthonian Center for Astrophysics. He has compiled all reported values of the Hubble Constant (H0), from 1924 to 2004. You can download the text data file, or just look at his plots. Most notably, see the two plots near the bottom of the page, which show H0 from 1970-2001, and again from 1996-2005.
We can see from the data that a value of 84 km/sec/Mpc would lie significantly outside the indicated range of reported values (the lines drawn on the plot are clearly not 1-sigma uncertainties, and look more like 3-sigma uncertainties, but are probably neither). It certainly appears, based on these plotted data, that 84 km/sec/Mpc is an unreasonably high value, and significantly unlikely.
Also keep in mind that all published values of H0 are here, not just those determined by the Cepheid P-L relationship. I think it is significant that the several methods used all agree in more or less ruling out a value of H0 that high.