A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Sean C
Date: 2016 Oct 7, 22:42 -0700
The duration of the eclipse will indeed vary based on the location of the observer. While I'm not exactly sure why, I suspect it is related to the parallax between different locations and is related to the discussion that Kermit, I and others had about the rate of change of the lunar distance to any celestial body dropping dramatically as the two bodies aproach minimum apparent separation. Here is a link to an animation showing an accelerated simulation of the eclipse. You can see that when the Moon first enters the path of the Sun's rays, the shadow is moving much faster than when it passes over the central U.S., and then it speeds up again as it exits. And here is a larger map showing the full path of the eclipse. The point of "Greatest Eclipse" shown on the map you provided does appear to be near the center of the whole of the path of the total eclipse. The USNO website (eclipses and transits section) has a lot of useful information on the subject.
I'm sure the more knowledgeable and eloquent members will be along shortly to confirm, deny or otherwise better explain what is going on.