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Do I understand correctly that the difference between
coordinates given by GPS/Google,
and an astronomic observation (assuming it is very accurate)
using Nautical Almanac cannot be so large as several miles?

So the difference in coordinate systems cannot explain the
change of coordinates of this island that we are discussing?

If both Cel Nav coordinates (the XIX century and the early XX century) are
to be trusted, they just indicate that
the island is shifting with time,
for whatever reason with the speed of few miles per century:-)

Well, we know examples of complete disappearance of islands in the Pacific
(Tabor=Maria-Theresa island and reef Ernest Legouve are some examples:-)
So why should we be so surprised if an island is shifting a little?

> Typically, the total shift amounts
> to a few tenths of an arcsecond (1-2 μrad, 10 meters) and is specified by
> the parameters xp and yp. The observational determinations are designated
> simply as x and y, and current values are available from IERS Bulletin
> A.18EO web site Past values can be obtained at the .19USNO Circular 179
> For most purposes we can set xp=x and yp=y (see 20
> section 6.5.2 or the IERS Conventions 2009 section 5.5.1). Several NOVAS
> subroutines require as input the xp and yp values for the date of
> interest, although, if the final accuracy requirements are no better than
> 1 arcsecond, these values can be set to zero.
>
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