You basically have two options :
1) Ditch the partitions, and just have all the tapes accessible within the library. Set each job to be an overwrite job, and ensure your overwrite protection period is long enough to prevent any tapes being overwritten before their time.
2) Keep the partitions, and point each job to a specific partition, you will then know which slot has been used by which backups, but you will as you've said have a LOT more jobs to create (though if you're using the default settings within Tools, Options, and the Backup Selections lists properly that shouldn't take too long.