IANAL but here's what I think an attorney who took the time to look the whole thing over would say:

The language in the contract (that you posted) seems pretty cut and dried, but I don't know whether that's actually going to hold up in a court of law. You entered a contest expecting the contest holders to hold the contest correctly. When the flaw was exposed, they did not honor it. That means your work was in vain. That's not in the spirit of the contest, thus the written words are only part of the story. A reasonable person expects that the company running the contest does so fairly. You seem to have not been treated fairly thus I think you have a case. I would imagine that, if you posted up a $500,000 lawsuit with $30,000 of reward and $470,000 of punitive damages, you'd hear from a different GE exec who has a very different POV.