Hashing Algorithm Integrity Validation I am developing an application that will need to store a very large volume of hashed data per user for which I want to ensure I am doing everything possible to maximize security.  At this point I believe I will be utilizing SHA3-512 + randomized salts over a yet-to-be determined number of iterations.

Is there a standard application level accreditation that exists to verify the security of my data encryption methodology, or is FIPS the only prevailing authority on encryption standards?
While there are no prevailing private entities associated with the accreditation of security standards, the NIST does provide the Cryptographic Module Validation Program that "validates cryptographic modules to Federal Information Processing Standards (FIPS)140-1 Security Requirements for Cryptographic Modules, and other FIPS cryptography based standards.." (http://csrc.nist.gov/groups/STM/cmvp/index.html)   

As I understand it, one could seek the status of a Validated FIPS Module via an NVLAP accredited Cryptographic and Security Testing (CST) Laboratory.

"Cryptographic modules are tested against requirements found in FIPS PUB 140-2, Security Requirements for Cryptographic Modules [ PDF ]. Security requirements cover 11 areas related to the design and implementation of a cryptographic module. For each area, a cryptographic module receives a security level rating (1-4, from lowest to highest) depending on what requirements are met." (http://csrc.nist.gov/groups/STM/cmvp/standards.html)

As such, one could leverage the FIPS security level validation from the NIST to publicly validate the security of their solution.