To the OP's original question: Since touring tires tend to wear out somewhat fast, and I'm cheap, I'm for wire beads all the way! The one time I carried a spare folding tire, I carried it 3900 miles for naught. I think you'd have to hit a pretty big piece of pretty sharp metal pretty hard to slice up a tire badly enough to need it. Carry a small roll of Gorilla tape instead, and look up how to boot a tire.
As far as tubeless vs. tubes: my girlfriend runs tubeless in her MTB and I run tubes in mine, and based on having serviced both I don't think I would ever tour with a tubeless set up. On the off chance you have issues and have to throw a tube in the tire it's a wet, sticky mess. But then, she might feel differently.
Patches work surprisingly well, and don't take too long to install. Word to the wise: read the patching instructions
carefully.
And since it came up: I'm a bigger fan of Schrader because it's much harder to break the stems off when using a frame pump.
