Extremely Low GPA - Should I Even Try?

Let me begin by admitting that my GPA is not decent ( 3.0-3.2) , or even low ( 2.5-2.8). Its an unforgivable 2.3.
Unlike many of my fellow low GPA MBA aspirants - I don't have any redeeming factors in my transcript. I can't claim a better GPA in my major, as this atrocious GPA is unfortunately my major GPA. I had poor grades in many elective courses as well - with the exception of an A in elective English and a B- in Compulsory English.

I struggled in early two years ( 3 year UG) and got extremely poor ( barely passing) marks , despite my best efforts. In my first year, I did slack and got disastrous grades. But in 2nd year despite sincere efforts, my grades did not improve. In final year - I literally put 200% in studying only to get meh (B-) scores. So technically though my scores did improve in final year - it was not like they went from piss poor to great - rather it went from disastrous to meh.

Back then, I kept on wondering, how on earth did I score such poor marks - 1st and 2nd year, despite my best efforts. But now - almost 9 years later, I know that I did not know then how to study. I had poor studying methods - all of which turned out to be counter productive rather than effective. My efforts though sincere were disorganized, clumsy, and led to almost nowhere.

For what it's worth, I graduated from one of the top liberal arts colleges of my country ( India), which was then affiliated to University of Calcutta - a university with one of the brutal grading curves in this country. Median GPA was 2.0-2.5 approx. Though I take full responsibility of my abysmal scores, and really don't want to shift blame the GPA curve of my alma mater for my poor grades - many of my friends who slacked off, partied their way through college at other colleges with relative grade inflation, came out with high 2s.

Ironically once I graduated my alma mater became autonomous and the median GPA rose to a dramatic 3.0 -3.2. C'est La vie.

I have since completed my Master's ( same college) with a 3.5 GPA, and also cracked a competitive All India Civil Service - have been employed as a diplomat. The govt of India has special programme for bureaucrats who want to study abroad - that includes grad programs like MBA, MPP etc. But with such a low GPA, I am hesitant to consider any of these programmes. Sure I have a very good work experience, and also some good recs, but I also have an unforgivable aggregate.

I am keen to sign up for some non degree programmes that allows students to continue to graduate programmes like MBA. Does anything like this exist? So far most non degree programmes demand at least a 2.5 GPA from UG, which I don't have.

To make matters worse - I majored in History - a major looked upon as ''easy''. Though in my country - STEM majors are actually more scoring with GPA rarely falling below 3. Humanities and Social Sciences are in fact not that scoring in most cases.

Do I have any shot at a good B School? Or have I shot myself of any chance? Any way I can make myself a more competitive applicant - when technically my UGPA disqualifies me from all grad schools? I know that I am basically asking B Schools to overlook my grades - and am depending solely on GMAT scores and work exp, as I have screwed UG as badly as possible without actually failing.