It's Catch 22. You want to get reimbursed for the loss of your receipts and the want the receipts to prove your claim. Consult with an attorney who can advise you on how to proceed. Use Find a Lawyer here.
The information provided is for general informational purposes only and is not intended to be legal advice. I am only licensed in the Commonwealth of Pennsylvania and I am not providing you with specific legal advice. The law changes frequently and varies from jurisdiction to jurisdiction. Being general in nature, the information provided may not apply to any specific factual and/or legal set of circumstances and/or the jurisdiction where you reside. No attorney-client relationship is formed nor should any such relationship be implied. The information provided is of a general nature is not intended to substitute for the advice of an attorney, especially an attorney licensed in your jurisdiction. Your question, although you may believe is simple, it is not simple. You require legal advice, please consult with a competent attorney licensed to practice in your jurisdiction.
You should start by looking at your contract. You may have released any claims related to theft. If the release is too broad a court might find it against public policy or unconscionable. Of course if the storage company was complicit I don't think a court will let them hide behind a waiver but proving complicity might be a problem. You can see if the county consumer advocate can help you. If not will want to engage counsel.
There is no substitute for the professional advice of an attorney who knows your case and represents you. My post is not, and may not be relied on as, legal advice and does not create an attorney-client relationship. Best wishes for a just and expeditious resolution.