This didn't really come as intuitive to me at first, but once I figured it out I realised it made a lot more sense than "center to board".
When you select the "Move" tool, you've got the options for alignment greyed out in the tool options.
To enable the alignment option buttons, you must first use the Marquee tool to select the region it should align to.
Once you've got a region defined, you can now align the layer according to the selected region.
Got the sauce? Let the photochopping commence!