What you could try is to deploy a BAR (like the SampleSales one provided with the install), deploy just the RPD and see if it allows you to restart the system, then you upload your RPD.
You do that by using "importServiceInstance". (Welcome to OBIEE12c: Using BI Application Archive (BAR) files )
Please beware: this command can also import and override catalog and security. So check 10 times the parameters to pass if you don't want to delete your whole catalog and security setup as well !!! (as you don't have backups)
You could still make a backup of the catalog by using runcat.sh in offline mode and create an archive of it, just in case.
Also something you can try just in case it maybe works ... export a BAR from your current instance, the BAR does contains the RPD, so with some luck the BAR will contains the broken RPD you can then fix or maybe it will contain a working older RPD. Maybe worth to invest 15 minutes and give it a try.
You might also want to check if your Linux/Unix guys make file system backups
EDIT: If by "which Backup" you mean you don't download the RPD on a regular basis yourself that is ...
It worked like a charm
Do we agree that you will look to setup a backup process for your OBIEE, right?
Already done ......