The specified user 'firstname.lastname@example.org' does not existI wasn't initially sure what that related to - I hadn't specified that account during the upgrade process so I went looking in the Services managemement console. The SQL Server service for the instance I was upgrading was configured to "Log On As" that account and it had been happily running prior to the upgrade.
This domain account did exist but to sanity check, the first thing I did was switched the service to use another domain account that also definitely existed and retried the Repair process. Same error. Then I spotted further down the list, another service had specified an account in the "somedomain\someuser" form. So I switched the SQL Server instance service to specify the account in that form (Down-Level Logon Name) instead of the UPN (User Principal Name) format (reference).
While I was waiting for the Repair process to run through again, I carried on searching and found this question on the MSDN Forums. The very last answer there confirmed it. The SQL Server 2008 R2 upgrade does NOT like user accounts in the UPN format.