Welcome to the Q&A Forum

You're in a good position with the site, because as far as I can see the business is well-liked and referenced. Definitely try and put the dampeners on those comment links and if you can, recommend re-investing budget in a more natural linkbuilding strategy that matches up to the calibre of the business. I appreciate this can be tricky though if it's a third party building those links. I think for the next few months I'd concentrate on improving the content on-site and using digital PR (definitely not press releases, but buzzworthy articles/content that people want to share) to build brand links. Hopefully the comment spam will be outweighed by those, if not a few guys here more experienced with disavows can advise if this is necessary.