You're mischaracterizing the situation. This is not a "paperwork snafu." A paperwork snafu is when something gets misfiled or perhaps a typo makes its way onto an itinerary.

You purchased a prepaid reservation, and then directed the vendor to cancel your reservation. Your error was in assuming that you would receive your money back. This is not the vendor's error. They are also under no obligation to provide you the product or service you explicitly and knowingly cancelled.

Once you accept the fact that the error is yours, you may be in a much better position to negotiate with the hotel directly. Call up the front desk manager, admit your mistake, and ask if they would be able to reinstate your reservation. Be flexible and willing to take any room. Recognize that they are under no obligation to offer you anything, and consider yourself lucky if the manager extends any sort of discount rate to you.