Do you normally carry your cards in your checked luggage?

It is an incredibly bad packing decision....and you are incredibly lucky that your bags were delivered to you.

If you have submitted receipts that should be enough. What was the total of the receipts submitted? Are they itemised? Is there anything about the receipts you submitted that - if you are being completely objective - look unusual/strange? If they are asking for actual proof of payment, it suggests that maybe they do not believe that all the receipts are all for your own purchases.

Also: have you considered claiming from your travel insurer?