First off, why no backups? System database are just as important to backup as your user backups. Please tell me you backup your Master database at least?

Second on custom logging, you would setup steps in your job to write to a table in a user database saying I did this, I did that, or nightly pull information from msdb.dbo.sysjobhistory into a table in a user database so you have a complete history, but if you do that and you know you need to go back 1 month, then just make MSDB store 1 months worth of data.