This can work, but it will actually be pretty tricky to generate the focused infrared beam that you need.
An IR LED, for example, sends its light in a huge, broad cone of light, maybe 20-40 degrees across. That means that it’s not going to be very sensitive to where you aim. It also means that the IR light is spread over a VERY large area– and very weak (too weak to trigger a phototransistor) over the targets that it does hit. One approach that might work is to use a telescope to project the light into a very small angle. (A video camera that can see IR light might make this practical.)
A second issue is that an IR phototransistor is sensitive to *any* source of infrared light that falls within its band of sensitivity. You will need to worry about sunlight and strong incandescent lights, as sources of shadows that can trigger the phototransistors.
It *may* be a better approach to use visible light. You could use “regular” phototransistors, and detect a carefully-focused flash from an LED, too. The difference is that you would be able to see a flash of light where you shot.
As far as limiting shots, either counting the time or number of shots is likely practical, but either method would require reprogramming the unit.
