Might lose out on job- flagged for being 6 hours short on degree. Already put notice at other job in? Help!

I have 146 hours out of 120 required for a college degree. I was there full time for 5 years, i switched my major 4 times and became pregnant my 5th year. I knew I neeeded to start working and ended up leaving school 6 hours short of a degree. I technically hour wise, am about halfway through a masters degree. Well recently I interviewed for a really high up position at another company. We never discussed that a degree was required, but I did put on my resume in parenthesis (5 years, full time at so and so university BA Sociology). I figured we’d have a conversation about it but it just didn’t happen for multiple reasons. One being that I assumed the degree wasn’t required. It didn’t say so in the description of the job. I got a job offer for an insane amount of money pending background check. I assumed we were all good. I put my notice in at my job and actually left, as of today was my last day. Well. I just got a call. Saying that they were able to see that I attended university for 5 years but didn’t graduate. I promptly explained to the HR lady, who then said she sympathized with me but that it would need to go through corporate HR and then also the VP who hired me. I am SO worried. I bring a ton of experience to the table including working for this companies biggest competitor. I’m hoping a miracle will happen. Can anyone give me their thoughts ? From the perspective of the employer. I’m pretty freaked out because now it means I just left my job at a Fortune 100 tech company to take THIS job and NOW don’t have a job at all. Please just be honest. I do plan to finish, but this is my current situation.