Addendum

This evening, Brandon hauled in the offending wheel to change the tube that was obviously trashed.  We pulled out the new, thorn-resistant tube and I pumped up the old tube to find the unfixable flat that tire slime couldn't fill.  I pumped, found the hole, and then watched as green slime bubbled to fix the flat.  Evidently the tube was not trashed - the slime had simply frozen into a solid lump this morning in my tire and couldn't slide around the inside.  And that is why I'm going to convince Brandon to retire to Tahiti.