Leave it running. No point in reinitialising unless something breaks.
You can (and probably should) leave your nightly full backups as normal full backups (without the copy only), especially if you may ever add differential backups to the backup strategy.
Edit: Damn, typing too slowly today.
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability