Go to mmOS proceed to your GAMES/GAMEZ folder and delete every PS3 UPDATE folder thats about 170mb for each of your backups. Since you have 30 games that should clear up 5.1gbs from hdd.
If you have doubts about this, your games will continue to work because I've done this myself.
"Ha! Man you're so funny you should be comedian, God Damn! Unfortunately I am I just hide behind the tears of a clown"- Verse from "Beautiful" by 3M1N3M