So I had one tube that had ripped open because it was pinched between the tire and the rim, and one tube that the stem top had come off because I had the pump head closed when I pulled it off. I took pliers to unscrew the stem top of the first tube and let the valve fall out the rip. Then I poked the valve through the other tube just behind the stem and dropped it through to screw the stem top on the other side. After patching up the hole I poked through to get the valve in, it seemed to hold air! Voila!

Now the question is: How dependable is this repaired tube? I'm carrying it as the second spare just to be safe.