For migrating moving a user in SharePoint you can use Move-SPUser
command in PowerShell
Move-SPUser -Identity "DOMAIN\oldusername" -NewAlias "Domain\newusername"
Technet link
Here is a previous post about collapsing a forest. Indicating that you should do a top down migration of the users.
You're on the right track. I prefer stsadm -o migrateuser as you have to pass a user object (from Get-SPUser) to Move-SPUser, which is inconvenient. The user's profiles will also migrate (which includes their MySite). Make sure you sync from the top of the forest on down. If you can't do that for some reason, disable the MySite Cleanup Job until your migration is finished and you're pointing your Sync connection at the single domain.
Intra-forest AD Migration with Sharepoint repermissions