I also thought you meant to put in a vertical divider in the bottom. To save space you might think about heating panels, they can be positioned on the sides or top of an enclosure and don't take up much room.
These are not UTH's but a whole other device.
With your height of 15" there won't be enough room for one of the swivel fixtures you're talking about (I have them in my 4x2x2, and they still look like they take up too much space)
Maybe a fixed low-profile fixture? they flush mount to the ceiling, made of ceramic and should be small enough for what you want. Make sure to use the gasket that comes with it, I had scorch marks on a cage I built using these with out them.