Lots of Severely Late Payments - Worth trying a Goodwill Adjustment?

Just a bit of background: I have around $78K in student loan debt spread over two smallish loans and one very large one. I graduated with my Bachelor's in Dec 2013, and have only two months ago gotten a salaried position in my field. I worked part-time to full-time as a grocery store clerk after about 16 months of unemployment (sending out between 30-40 applications/resumes a month, so not for lack of trying).

A lot of fumbling and not understanding clearly how the student loans worked, I have about three and a half years of a terribad late payment history. I spoke to multiple people at my student loan providers but was never able to get them the proper paperwork in the proper timeframe. I did get many forbearances and deferments, but that didn't help the overall goal.

I have gotten everything relatively sorted out now for the future, got a Income-Based Repayment Plan for the highest of the three loans, am making payments twice a month, and have a budget set. I'm trying to improve my credit score in order to be able to purchase a house in around a year (rent here would cost nearly twice what a mortgage on a reasonably priced house would cost). My question is, is it worth negotiating with these companies to get a Goodwill Adjustment to remove some of the late payment history? I have two loans with Great Lakes, and one with Navient. Thank you all in advance!