100% in agreement with Alan here. Reconsideration request and the disavow tool DO work and we have used them on 2 clients with proof. It can take anything from 4-12 months for you to actually see the positive results, they do work. Try and get the links removed first BEFORE using the disavow tool because Google wants to see that you have made an effort to get them removed rather than just take the easy way around!
It is true that you won't get responses from them all, especially if it is article websites where the webmaster rarely does anything on the site itself. That is when you use the disavow tool, just make sure that you are 100% certain that the links are doing your website harm.
Be honest though and look at which links are spammy and do your up-most to get them removed first. It takes time and a lot of effort but it will work....eventually!