Well, I may be out of this ride. I need to go to bed... It's been a long day. I can't stay up and monitor for a decision much longer.
I didn't replace the rear tire. It was too firm to let go, so I added more Tufo Extreme Sealant to it. I couldn't hear it leaking like I did at the airport, so I think I'm going to declare success.
Also, I did a retread of the tire, coating nearly the entire contact patch with ShoeGoo after scrubbing it down with a ScotchBrite pad. By morning that tire should be bulletproof.