UPDATE:
I phoned D-link support they escalated to the highest tier. The answer the technician gave me was not very satisfying.
According to him, based on a couple other reports, the S3 app that comes packaged with the DNS-325 has a 2 GB file upload limit.
Really? Surely many people have >2GB to back up in total. He may be confusing it with an old bug that limited single file size to 2GB or less, but this model and firmware is not affected by that bug.