Pipe fixed! I tried my best to apply all the good advice received here, but I think this was one of those things where I had to make some mistakes in order to understand the collective wisdom. Here is a brief summary of my learning experience.
First of all, I realize that I could have avoided this leak very easily be removing the hoses when I heard that winter was coming. At least this experience forced me to locate the main water turn-off in the garage, which I plan to label ASAP. I also found the turn-off by the street, but understand that it is illegal for civilians like myself to mess with it, at least in our town.
A fellow mustachian who may or may not go by the name Hamster, offered to lend a hand, as he had some basic soldering experience and tools. We initially considered replacing the copper with PEX, but made a decision to go with copper, I think because it would have been slightly cheaper. We later regretted this decision. We found a replacement siphon faucet, deciding to go with an 8-inch rather than 10- inch length to reduce the need to bend the copper supply pipe coming from the ceiling. While well-intentioned, this made it virtually impossible to solder the joint closest to the external wall, requiring us to solder that part before placing the faucet through the wall. Not a big problem, but not ideal. We set about soldering the joints, and if we had superior soldering skills, everything would have gone swimmingly. Unfortunately, we kept having small leaks, which then required us to turn-off the main water supply, sweat off one or more of the joints in order to get all the water out of the pipe, and then begin again. What should have been an easy job was taking hours, and, pressed for time, we went back to the store and purchased press-fit couplings which worked like a charm. One soldered joint remains, connecting the pipe to the faucet, and if we could start over we would have instead installed one of the joints that screw right onto the faucet. We actually bought that part on the last trip, but since that joint was holding firm, we left it in place. Photos below.