That is a really tough, but all too common story. I definitely would not start over on a new brand if that's the case. Would it possible to switch from Brand.com to brandwidgets.com? Just wondering.
Either way, before I scrap the domain or hire this high priced company, I would check these guys out: http://www.linkdetox.com/plans-pricing/. You obviously are smart enough to use Moz so I think this tool could help you disavow the bad links. It would take a while to see the results but using a tool like this to get rid of bad links would be the first step I take before you pay a kings ransom to a firm (assuming you cannot afford) or (gulp) shut down your business (<------don't do this!!).
p.s. I'm always a little skeptical when people push a product on me so for the record, I in no way benefit from the product i mentioned earlier. There are plenty of competitors who do what they do as well.