I'm answering my own question.
Apparently this is one of those rare cases when the physicist must doubt what he observed -- or what he thought he observed -- and believe the numbers his theory yielded instead.
From further experiments I've noticed that the ice tends to form thin plates inside the supercooled water once the crystallization process starts -- this form of ice is apparently called dendritic ice. When the starting temperature of the water was about $-10^\circ$C, the resulting ice-water mixture still contained a lot of water by the time the process finished, and most of it was trapped between those thin ice plates. The latter fact would make it hard to measure the mass percentage of water exactly.
I've found some scholarly articles studying this process -- mostly in the context of formation of ice plugs in pipes. In [1] they measured the temperature at a number of points inside a capsule full of supercooled water during ice formation. From the time-dependent temperature profiles in the article it is obvious that my model above (that energy released by the freezing ice heats up all of the water and ice) is completely wrong. The process happens so fast (at a rate of a few cm/s, depending, among other factors, on the temperature), that the heat transfer between the already frozen (thus heated to $0^\circ$C) and still supercooled regions is practically negligible.
However, based on the observation that ice and water appears well mixed in the already frozen region, we can put forth a new model: the released latent heat of fusion is used up locally and quickly in the boundary layer of the expanding frozen region. As a particular region at the boundary freezes, it heats up rapidly to $0^\circ$C (or close to it), and heats up the water surrounding it. Since the ice plates thus formed are relatively close to each other, the resulting region containing ice-water mixture will mostly be free of temperature inequalities, and those inequalities that do exist will be damped quickly. Therefore the thermal profile of a volume of supercooled liquid undergoing freeze-out will consist of two flat regions, with a relatively sharp boundary between.
It would be quite interesting to look at the process with a thermal infrared camera. Such an observation could confirm or reject the model above. To my knowledge, no one published such an observation -- if such a publication exists, I'd be very interested in seeing it. A video made by such a camera would be especially enlightening.
With some simplifying assumptions (spherical container full of supercooled liquid with uniform temperature, and a single nucleation source at the center), the simple model above could be made quantitative, but I haven't done that yet.
1 Juan Jose Milon Guzman, Sergio Leal Braga: Dendritic Ice Growth in Supercooled Water Inside
Cylindrical Capsule, 2004
Best Answer
First of all, when you say that trying to crack a pipe is hard work, what you probably mean (in physics terms) is that it takes a large force. But that doesn't necessarily mean that it requires a lot of energy. The energy used in a physical process like that is equal to the force times the distance over which the force is applied, and you don't have to push very far in order to crack a pipe. In fact, the pipe barely moves at all before it cracks, so even though the force required is quite large, it only acts over a tiny distance, and therefore it barely takes any actual energy. What little energy is required can come from the water itself.
To explain the "how" you have to consider molecular interactions. (Well you don't have to, but I'm going to.) The energy of each pair of water molecules varies with the distance between them, in a manner shown (approximately) by the following graph (from Wikipedia).
Lennard-Jones potential http://upload.wikimedia.org/wikipedia/commons/thumb/5/5a/12-6-Lennard-Jones-Potential.png/800px-12-6-Lennard-Jones-Potential.png
You'll notice that there is a certain distance at which the energy is a minimum. This distance represents the "natural" equilibrium distance between molecules when there is no pressure. However, when the water is under pressure, the molecules get pushed together (because pressure is roughly akin to force), so their actual distance will be a little closer than the minimum of the graph.
Water has the unique property that its "natural" density at a constant pressure reaches a maximum at a certain temperature, around 4 degrees Celsius, and that its frozen form (ice) is less dense than its liquid form. In other words, the equilibrium intermolecular distance (the minimum of the graph) is smallest at 4 degrees Celsius. If the water temperature is going to drop below 4 degrees Celsius, the minimum shifts a little to the right, which means one of two things has to happen either the water expands (if the intermolecular separation stays with the minimum of the graph), or its pressure rises (if the intermolecular separation creeps up the slope of the graph).
Now think about the situation in a pipe. As long as the pipe stays intact, the water can't really expand at all. So the only option is for the pressure to increase. As the pressure increases, the force on the pipe increases as well, and you'll notice that because the slope of the curve is very steep, the force increases very rapidly. At some point, the force becomes large enough to overwhelm the bonds that hold the atoms/molecules in the pipe together, and at that point, the pipe cracks. Notice that in this theoretical model there's no need for any part of the pipe to have moved, which means the pipe could crack without any energy being used. (In practice, there are other things going on that do make it take a tiny bit of energy.)