Hi, from reading through this thread I think you are safe getting rid of those full backups. Save the most recent one, if you are nervous. Then, consider finding the cron job that is making daily backups and stop it.
Dreamhost makes incremental backups of your databases. Go to goodies, mySQL in the panel. There is a “restore DB” button you could use.
Your database seems really large. You might want to clean it out a bit, get it to a more reasonable size.