Volume password challenge in Migration Assistant
I resolved the Volume Password issue. I did two things, so I don't know which of the two actions resolved it or if they both played a part together. If you encounter the same Volume Password issue, maybe your scenario will resemble mine and this will help you, too.

The accounts on my target iMac had issues with their iCloud configuration. I reentered the authentication for those iCloud accounts.
Returning to the Migration Assistant, this time when I ran through the wizard I waited for the source accounts and documents to be identified completely before advancing to the next screen which prompted me to create a password for the administrator account I was migrating. Formerly, I created the password on that screen before the previous screen completed identification of the file sizes to be migrated, while going back and forth between the two screens until the file sizes were calculated completely.

This time, I waited until the file size calculation was complete before advancing to the next screen for creating a password for the administrator account I was migrating.
The next screen is where, formerly, Migration Assistant challenged me for a Volume Password. This time, the prompt didn't refer to a &quot;Volume Password,&quot; but instead said it needed authentication for an account authorized to create a new user. I realized this meant an account on the target machine. That must have been what it was trying to do at this point before. I still don't know why it didn't work in the former case, because I know that all the passwords I tried included those target machine accounts, too, and they didn't work. This time, instead of challenging for a Volume Password, the screen identified for me the name of an administrator account on the target machine.
I supplied that account's password and the migration began.
So, it works now. As an extra reward for surmounting this surreal problem, while I was fixing my iCloud synchronizations I got the attached error message. Mind you, there is only one iMac on my network. The source for my migration is a MacBook Pro.
This is a perfect OSX koan and it is my single favorite error message ever.