OK, I need to apologize to wise guys everywhere. The problem with my bike tire was a real leak, and no one let out the air while I was at lunch yesterday. After sleeping on the problem, I tackled the tire and tube again today, and found a small leak. I successfully patched said leak, and reassembled the tire, and mounted it on the bike. After giving the patch a while to show its effectiveness, I was satisfied it would hold.
I did a 17-mile route today that was basically flat. While I was not trying to ride at any set pace, I did take my GPS today, and saw that I averaged about 12 MPH. Again, I'm satisfied with that. I felt good at the end of the route, except that the bottom of my feet felt numb from the pressure on the pedals. I'll get the new Shimano pedals and clips on later this week and see if that helps some. Tomorrow I intend to take Max in the trailer to see how he does on a longer ride of about 2 hours. I'll need to give him a break halfway through, and I may need to give him more protection from the sun, but we'll see how he does.