Sorry to hear about your website pain.
I am on the other side of the spammy link fence. I paid for an seo in 2011 to work on a site. They used black hat seo methods such as link from places such as Fiverr, yet they used digital point forums for links.
Then Here it is 2012. and Google hates me.
2013 I am a member of Moz. The best move I have made for sure.
I have done what you have and updated a disavow txt file.
I have heard many different strategies. Some say you will never recover from a non manual penalty. Some say clean up bad backlinks then replace them with good quality natural links. Then I have had some say clean up backlinks, create new ones, and then wait till the next update.
I have started with zero citations to now I have 200 or so. I do not have a bunch of backlinks, about 230, yet I am trying to gather high quality links.
So I think if you once ranked with bad backlinks, you must replace them with good quality backlinks. Other sites are ranking, so maybe use the explorer tool to see what the competition sites are using for backlinks, and see if there are any opportunities.
Best of wishes