The good news: The hot water pipe to the kitchen faucet is now connected again, and I'm now the owner of a brand new Ridgid pipe flaring tool.
The bad news: The pipe is connected via a ½" flare nut to a ½"-flare-to-½"-FIP union to a ½"-FIP tee to the faucet, with the unused arm of the tee capped off, and the pipe flaring tool cost $40 we could have done without spending (but it's one of those tools that when you need one, you NEED one, and nothing else will do). This godawful plumbing clusterfuck is necessary because the ½"-MIP flare nut that fractured was pure 24-karat unobtainium, ½"-flare-to-½" MIP unions were conspicuous by their absence from everyone's shelves including the regional specialty plumbing supplier, and while I had in my hand a perfectly good ½"-flare-to-½"-FIP union that we stumbled across in Walter's garage while looking for the mythical ½"-MIP flare nut, ½"-MIP-to-½"-MIP unions were again not to be had for love nor money. Why did the faucet terminate in ½" pipe threads in the first place? Probably because the manufacturer assumed that everyone who was going to install one would be hooking it up with reinforced vinyl tubing instead of copper pipe.
The gripping hand is, it ain't elegant and it ain't pretty, but it works, and it doesn't leak.
Update, Thursday Augnst 26 10:15:))EDT
I just checked last night's work, and it's bone-dry, not a single drop of leakage, not so much as a seep. It's drier now than it's ever been while we've lived here.