It's a real self-defeating thing to do but, if you use proprietary software systems, always have an "analog" backup of your own design for times like this. Something that might be laborious and annoying but, in the event of the unspeakable, could be migrated to a new system manually or simply archived in searchable manner. .csv files, .pdf, whatever you can manage and demand clean export options from your software developers. You never know when someone could drop out of biz or pass away, taking the knowledge of those unique file extensions and coding, and your data, with them forever.
We've been slacking a little on this and I need to get back on it and seeing your nightmare situation just reminds me all the more.
Good luck man. This does indeed suck. I freak out if our system is down for even a few hours during business hours.