While I was dusting off my old external hard drives to use as a start up disk, I got an email from my son with a suggestion that proved to be very useful. He suggested I try Command R while rebooting. This proved to work well. Not only did it get me out of the El Capitan install loop, it also presented me with a very useful menu. Among the choices were "Install operating system from the internet" and "Restore internal hard drive from Time Machine."
I chose the latter, as it would also erase the hard drive before restoring. I hoped this would remove the 400 gigs of unexplained content on the drive. In about an hour, the iMac was back up and running identically to how it was about a week ago, and the 400 gigs of unexplained disk content was gone. The hard drive was back to the 65 gigs of content that was normal for this computer.
The only gotcha was that the Time Machine backup was from 28DEC14. I have no explanation for this. Time Machine had been working normally all through 2015. Checking Time Machine today showed it has been backing up normally yesterday and today. There is a gap in backups between 28DEC15 and 1DEC15. I thought Time Machine erased files from oldest to newest when short on space. It seems the El Capitan installer must have been trying to scavenge space on the Time Machine hard disk. I don't have any other guess on what happened.
The restored iMac is in better shape than expected. My wife works primarily through email. While Time Machine restored her email only from 28DEC14, she realized she had all her 2015 email on her iPhone and online through our ISP. Surprisingly overnight, her email files on her iMac updated themselves with no action from us. That means she has all the files she attached to email or received from email. She is only missing files she created on her iMac and did not email. She can also restore her music and photos from her iPhone or from me.