Problem solved ...
I had been using the binary distribution of ImageMagick for cygwin (6.8.1).
I un-installed that, then downloaded ImageMagick-6.8.3-7.tar.gz and unpacked. Ran './configure --without-perl' and make, then make install. No problem.
Minor tweak to my project Makefile, built without a hitch.
Program now runs fine with large images.
I can only assume there's something about the 6.8.1 cygwin binary distro that limits reads to 256K.
Thank you again for your help.