When I got home, the leak was still under control, but was clearly worse. The dripping was enough of an annoyance to myself and the other members of my household, that I figured that I could make the repairs tonight before I went to bed. However, I unfortunately learned that even more of my pipe was deteriorated than I thought. As I tried to remove the connection at one joint, pin-hole sized sprays started shooting out all along the pipe--including beyond the shutoff valve.
I turned off the pump for the house, but it was too late to go to the stores for parts for the much larger system that I now need to replace. I think that I have it figured out so that both this problem and future problems on this line can be solved. I setting my alarm early so I can get the parts right away and possibly even have everything fixed with enough time for Janelle to finish getting ready for work in the morning.
I really hope that this doesn't suggest that we will have more problems in areas that are more difficult to get to.
[Edit: Although it took me longer than I thought, I got the section fixed and the water running in the morning.]