Well, this sucks...
Arduino: 1.8.5 (Windows 7), Board: "Arduino/Genuino Uno"
Sketch uses 20190 bytes (62%) of program storage space. Maximum is 32256 bytes.
Global variables use 16787 bytes (819%) of dynamic memory, leaving -14739 bytes for local variables. Maximum is 2048 bytes.
Not enough memory; see http://www.arduino.cc/en/Guide/Troubleshooting#size for tips on reducing your footprint.
Error compiling for board Arduino/Genuino Uno.
This report would have more information with
"Show verbose output during compilation"
option enabled in File -> Preferences.
So, as I understand it, the code in Post #14 works with 720 bytes. But if I give it all 16kiB of data, the program is too big. I guess I'll have to divide it up into 1kiB chunks.