I figured out the conflict. The Fancybox option in the NextGen Gallery Optimizer must be turned off, and the Easy Fancybox plugin must be installed. Then do as Easy Fancybox suggests, and set the code in the options of the Gallery to class=”fancybox” rel=”%GALLERY_NAME%” and the get then wraps.
Please note that the original FancyBox for WordPress plugin has to be deactivated for any of this to function, and that is where I had a struggle.