Bigger challenge than expected

I am performing reputation management for a customer and although I've been able to get new url's to show when the customer is searched in Google and push down most negative url's, but there are 2 high authority url's that will not go away.
One url is an online local magazine article and another url is a gov article.
I know these are 2 high authority url's and that's why they are sticking.
I can use some advice here.

The advice I could give you would depend on what you've already done. I typically start with the easiest and quickest methods and move to the most difficult and expensive methods if the quick and easy doesn't do the trick.

Have you tried premium content like Huffington Post? Any press releases? Guest posts/sponsored posts?

I did the quick and easy, but not HPor press releases. I will try them next. Thanks