pulling fuses should work - as long as you are pulling the right fuses...

for a battery to discharge overnight, you need to have a consistent draw on the battery for the extended period of time, or a quick short - the quick short will leave burnt marks...

all of this assuming that the battery is a good battery, and you say that you have replaced the battery couple of times... but, if the battery is not good, it may discharge itself from internal malfunction, when the chemicals leak into each other's chamber - the so-called dead cells, or even shorted out cells...

setting up a camera - are they expecting a little gremlin actually do some physical harm to the car??

do the ultimate test, at night (or, whenever you are finished with the car for the day) disconnect the negative terminal of the battery completely from the car (i hope you have a garage) and in the morning, when the car would have been dead otherwise, try reconnecting the thing and then try starting the car... if you have a multimeter, measure the battery at night, and then measure it in the morning, before attaching the terminal...

this test will eliminate the battery from the picture, and then you can concentrate on the car...