Not paying back sign-on bonus due to employer breaching contract

I received a signing bonus after completing 3 months of work with my employer of $10K and then I get another $10K at 12 months. Contract states that if I leave before 15 months I have to repay the bonus. I am not going to be with the company for 15 months so I had just planned to give it back when that time came. But we have had tons of issues since I have been working here. Unsanitary working conditions with roaches and rodents in the office (I have complained and documented them several times too) and through my personal investigating and over 3 weeks of arguing with payroll realized they had underpaid me $30K in the first 4 months of my employment. My question is in this scenario could I easily just tell them I am not going to repay the bonus due to all the problems with my employment with them and that being the reason for me leaving. Essentially they breached the contract already by not paying me how the contract stated I should be paid. They admitted they were paying me wrong too but again it was after I fought with them for 3 weeks to figure it out and the numbers they were sending me to check my pay were way off (in one month over $100K difference in what the numbers were and what they were telling me they were). Do you think this would be a reasonable request and would hold up if we actually had to fight it out? Also when I leave I am required to give a 90 day notice which I expect to still honor but don't want them withholding pay to recoup the signing bonus on my last payroll before I leave.