I took my car into the shop last Monday, telling them to keep the car until they discovered the problem.
Unlike the last time I took the car in, they could see the charging light, as well as hear the chattering relay (thanks, Dave). They had a hard time hunting down the problem, though.
Three days later, the car was fixed. The shop replaced the alternator they had installed, but the replacement overcharged. They then switched to a Motorcraft alternator, which finally worked. They still kept it overnight one more night to cold start it the next morning to be sure it was fixed. They also replaced the battery, but since it was the original seven year old battery, not unexpected. Not welcome, either, but not unexpected.
I picked it up Thursday and ran errands, ran errands Friday, and today I took it on an out of town trip. Everything tested out, current car crises resolved. Thanks for suggestions and advice last week. It helps to work from knowledge.