"He's going in a straight line, ...I measure 625 nm in a straight line"
Not unless he has a motor boat. Remember, the wind is usually coming form the wrong direction and if he has to tack all the way, 625 miles becomes 625 times 1.4 (angling off for the tacks) or 875 miles for the shortest course run.
It is all true, however the wind was not really a headwind - at least it was not from Monday until about Friday or so. Here is the GRIB picture from Monday and the one from Wednesday (one data point, midnight of that day).
The winds are SE during the early part of the track, turning NE later. Not much of the "on the nose" component, so there shouldn't be a need for tacking.