I don't think hashes will protect what you're wanting to protect.  People with only the hash should be confident that the money is not being fabricated, but whoever is doing the hashing can fake it, and unless they are forced to prove that the full accounting generates the hash, there is no way to know.  So you might as well just append the unencrypted total to the hash of the sorted list.

You could store the map in "unary", in other words { (A, 5), (B, 2) } would be stored as "AAAAABB" (lexicographically sorted before expanding)

Then encrypt with a public key.

The length serves as an indicator of total value.  If you use a block cipher in counter mode then whoever has the private key could decrypt portions to prove that certain keys own certain coins, without having to divulge the entire ownership map.