I was having issues with other page elements overlaying my FancyBox images when they exceeded a certain size. The site logo, search box, and most of the header navigation was sitting in the way, to the extent that I couldn’t even click the “close” icon in the top right corner of the FancyBox.
I fixed the problem by editing all of the CSS z-index values in /skin/frontend/default/hellominty/css/custom.css by simply adding 2000 to each value (so, e.g., z-index: 90; would become z-index: 2090; etc.). This solved the problem and now things are working normally.
Not sure if this is an issue with other themes or just HelloMinty, but I thought I’d mention it.