Does anyone have any hypotheses on why there's a difference
between the on-screen and calculated MPG?

Several possibilities come to mind.

1) Applied computer technology is not necessarily precise - some is and some isn't. I am amazed at how well the computer technology in the FEH works , but have limited belief in its precision. (I am a computer scientist and supposedly know what I am talking about.)

2) Apparently the computer makes some assumptions about each tank - the primary one is that all full tanks are the same. They aren't, of course, as the manual points out several times. Even a few tenths of a gallon can make a significant difference in the calculations. The manual recommends determining the message center MPG on the basis of several tankfuls which should even out the variation in tanks.

3) During the Dearborn "parade," I asked my engineer (possessive, aren't I) about the basis on which the display MPG was calculated. I got the figure 2000. I thought I heard him say "miles." This would be consistent if the computer updated the estimate every mile. In any case, to the degree that 2000 data points is considerably more than a single tank, the average includes previous tanks.

I might say that point 3) is consistent with my own experience. When I took delivery of my 06 FEH 2WD, about 1000 of the first 1500 miles were highway. (Not the way I would have done it if I had had a choice!) When I started driving in city environments, the display MPG climbed slowly from 31.7 to its current 36.8 at 3800+ miles. Calculating MPG separately gives me 40.2 and 40.7 respectively for my last two tanks. So my computer MPG is lower than my actual, which differs from the other reports here.

Can the computer be set for a base other than 2000 data points? My engineer said no. It can be resect to factory default, of course. This was offered to those at the Dearborn event. I declined.
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06 FEH 2WD "Sainte Marie"