SSRS Domain Migration
I would go back to testing and find out why the SID migration did not work. It is a migration Microsoft supports with Active Directory. I would suggest engaging the support for the Data Center you are moving to for assistance. (or even Microsoft...)

If the SIDs cannot be fixed your only option is going to be recreating the accounts and permissions. Thinking about it, since Data Center moves could be in your future again (or at least the companies) you might rethink some of those permissions where all of it is groups, even if you are dealing with one account currently.

You can execute queries against the ReportServer instance to get those permissions, but not one to modify the logins and such.