They can actually exert a good amount of force, but I don't know what kind of force is needed to get those doors open as I've always gone the sliding glass door route. The locks (at least on the sliding doors) are more to keep unwanted hands out more so than keeping the inhabitants in.
In the mean time, if you haven't found a solution already, you should be able to find a luggage strap for pretty cheap that can be tightened around the enclosure that should help keep the doors closed until a more permanent solution from AP arrives.