So I finally got a call from Mine's Takayanagi-san to update me on my car.
Here is what he told me that they've found so far:
Apparently, they found most of the water in the cooling system, gone! So they suspect a broken hose somewhere. No visible damage anywhere, so likely they will have to lift up the car and/or remove the engine to be sure.
Luckily, I only drove for about 10 minutes once I saw the smoke so there is unlikely to be any damage due to overheating, however Nakayama-san will be inspecting the head of the engine to make sure there is no damage. (keeping fingers crossed, that sounds expensive!!!)
If the leak was from a hose somewhere, it would have happened very rapidly, as I don't recall seeing a puddle of coolant in my garage area. So it would have happened that day when I drove to Yokosuka.
Additionally, they found that the water that remained, was rusty. This is probably my fault, I can't recall the last time I had the coolant changed - I thought it was a couple of years ago - and I've never had any cooling issues. Takayanagi-san doesn't believe I need a new radiator, but it (and the whole system) will simply need to be flushed out thoroughly.
By the way, I've circled where I saw the smoke/steam coming from:
In any case, I will let them first diagnose exactly where the leak is coming from, but assuming that it is a hose that gave way, I think I will have to replace some of those hoses back there with something stronger. Steel braided looks nice, but my understanding is that silicon hoses are just as strong and reliable (so long as you use the proper clamps) and steel braided's drawback is that the braiding prevent you from finding the source of a leak quickly. People's thoughts on this? If I do silicon, what color? Blue or black? (note I already have the Samco set for the radiator, in blue).