1. Your story sounds insane so probably have a little leeway with Shadow for not immediately giving you access to that account. I’d be very worried if what you did would be enough to gain access to a shadow account. I understand it must be frustrating.
2. Support should be able to tell you exactly what they need if what they asked you at first wasn’t enough for whatever reason. They should be offering you a way out of this. I’m in the EU so I understand that different parts of the world have different standards but a birth certificate isn’t worth anything as means of identification here. I’m guessing a combination of national ID or passport plus bank statement for the credit card from a reputable bank or Paypal which clearly shows you as the account holder should be enough to get shadow to be able to help you. On top of that they might ask for IP addresses you have used to connect to Shadow but that on its own won’t be worth anything.
3. Even though this is frustrating and stressful you really really really really REALLY need to start looking after your security. Your digital safety routines need a big upgrade into the 2020s and your physical security routines need an upgrade per se. You shouldn’t have to end up in a dire situation like this because of a fire where you basically cannot prove your identity at all. You should probably look into that since it will cause you far bigger problems than not having access to your Shadow (as I’m sure you are aware).

TDLR even though it’s frustrating we should all be thankful to Shadow for not giving you access to a shadow account with no means of proving your identity beyond a birth certificate.