I haven't used version 4 auth, yet, for multipart uploads (my code uses v2), but I did find this:
x-amz-content-sha256
When using signature version 4 to authenticate request, this header provides a hash of the request payload. For more information see Authenticating Requests by Using the Authorization Header (Compute Checksum of the Entire Payload Prior to Transmission) - Signature Version 4. When uploading object in chunks, you set the value to
STREAMING-AWS4-HMAC-SHA256-PAYLOAD
to indicate that the signature covers only headers and that there is no payload. For more information, see Authenticating Requests Using HTTP Authorization Header (Chunked Upload).
http://docs.aws.amazon.com/AmazonS3/latest/API/RESTCommonRequestHeaders.html
Obviously, chunked and multipart are not the same thing, but perhaps this value is also appropriate for a multipart upload request, or will generate a new and more helpful error message. The documentation seems unfortunately sparse in this case.