UPDATE: Thank you for this advice. My girlfriend was able to recover her account by telling Oculus support that she wanted to buy a product, but wouldn’t commit to it unless she knew her account would be usable.
If you bought one of those products, could you then return it for a full refund after getting the account unlocked? You might still have to pay for shipping costs, but I imagine that checking and repackaging a product costs Facebook money too.
Perhaps Facebook would lock the account again after processing the returned product, but that should give the user enough time to export any useful data from the account, and to provide alternative contact details to any Facebook-only friends.
Sad to say, that's the only way other than knowing someone who works for these companies :(