High Energy Metal Halide Bulb Heat

You could build a mechanical shutter operated by a servo motor and controlled by a microcontroller easily enough, but there is another issue.

Your 400W of input power is being turned into light and heat. I don't know what the efficiency of your proposed bulb is, but even if it was as high as 25% (dubious) you'd still need to dispose safely of 300W of heat continuously. When the shutter obstructs the light the waste heat will probably ramp up to almost the full 400W because most of the 40k lumens are going to be converted back into heat.

Have you looked for high power LED's (or LED arrays) that can generate the kind of light intensity you need? LED's can usually be switched on and off pretty much as required, and they're also generally more efficient than other light sources.

1 - Location of the fan is irrelevant, since the airflow is driven, rather than occurring due to convection. Actually, putting the fan under the box rather than on top is best, so that the fan never gets heated by the hot air it is exhausting. At any rate, you want free air flow through both top and bottom. Note that this directly competes with your desire to reflect as much light as possible. Whether 240 CFM is adequate I don't know, but I'd suspect you'll be OK. No guarantees, though.

2 - Depending on a spray-on paint to fireproof the box is a really bad idea.

3 - Putting a probably-flammable layer of reflecting paint on top of the first layer is an invitation for the reflecting layer to catch fire. Your problem is that there is no obvious way to determine the reflectivity of the reflective paint in the infrared, and that is where most of the energy is emitted by the bulbs. Metallic silver by itself has excellent reflectivity into the IR, but that does not necessarily imply that your paint does as well.

4 - If you really think you'll be present for 10 hours continuously, well, all I can say is that I admire your bladder control. Not to mention your willingness to go hungry.

5 - As I recall, you're trying to illuminate a 3 x 5 foot area. If you want a fairly uniform illumination level over the entire area, you will need to make a tradeoff on box size. The closer you put your light source to your test area, the bigger the box (or at least the transmitting aperture) has to be. With a larger separation you can use a smaller box, but then you lose intensity. Also (and this is important), the bigger the box the harder it is to control exactly where the air goes, and the harder it is to guarantee that there are no dead zones/hot spots.

6 - In line with 1 and 5, just exactly how big a box were you figuring to make?