To minimize read-only time, I'd change the order a little.
1. Full Backup
2. Copy backup to new server & restore with NORECOVERY
3. Set to read only
4. Differential Backup
5. Copy differential to new server, restore WITH RECOVERY
6. Set to read/write.
It doesn't make sense to restore the full & differential in one batch. You might as well just do a full backup & restore.