YouTube claims that I haven't been able to prove that I have commercial rights to this video of Superman.
I've never heard of YouTube doing this. If this is the US, then something is missing here.
If YouTube wants safe harbor under the DMCA, my understanding is that they can't require that you prove you own the copyright. Instead, they have to let you publish the content, then wait for someone to file a DMCA complaint against you. Then, once you file a counter to it, YouTube must allow the video to go back up. I'm not aware of any point in the process where YouTube gets to determine who owns the copyright.
You didn't mention anything about anyone filing a DMCA claim against you, so I'm totally confused where this requires to prove your commercial rights comes from. Ultimately, the answer here is probably "get a lawyer." Especially since you mention "commercial."