An earlier record of Europeans shooting passenger pigeons (“doves”) that Joel Greenberg found but was not able to get into his book:
A second voyage left France in 1564 under the command of Rene Laudonniere. At the mouth of the St. Johns River where Jacksonville now stands, he founded Fort Caroline on June 22. It, too, would fail, as the Spanish, aware of France’s intentions, sent a fleet about a year later to slaughter or imprison most of the inhabitants and destroy the structures. Laudonneire managed to escape, however, and wrote of his experiences. Sometime between January 25, 1565 and May 1565, there occurred the earliest instance of Europeans killing passenger pigeons that I know of:
“In the meantime, a great flock of doves came to us, unexpectedly and for a period of about seven weeks, so that every day we shot more than two hundred of them in the woods around our fort.” ( Rene Laudonniere, Three Voyages (translated, edited, and annotated by Charles E. Bennett), Gainesville: The University Presses of Florida (1975): 114.
http://www.birdzilla.com/blog/2013/12/29/earliest-instance-of-europeans-killing-passenger-pigeons/
The exact location of Fort Caroline has never been identified, although at least one archaeological attempt to find it is underway. Recently, some people have even claimed, apparently without showing much evidence, that it was actually in Georgia.
I just realized that this account was also in Schorger’s 1955 book The Passenger Pigeon: Its Natural History and Extinction.