If it's just some kind of light for day/night, it doesn't have to be in a dome fixture on top of the screen at all. It can be a regular table lamp nearby or something, or a strip of those LED strip lights (you can get them on Amazon for cheap) stuck so they light the inside of the cage.
Reasoning is, you need the same amount of heating at night as during the day, basically. So unless you want to swap bulbs in and out all the time (doesn't sound like a satisfactory long term solution), just use the nighttime heating setup all the time and get a day/night cycle from somewhere else. It doesn't have to be a bright spotlight from directly above.