As somebody who never understood the rationale behind entrance scores being the sole criteria for screening candidates for an MBA, I understand your concerns. But rather than looking for an institute that offers you MBA without entrance, I would suggest you to look for one that doesn’t solely rely on your entrance score.
One such institute is SOIL Institute on Management, Gurgaon. It does not judge your fit into the program only based on your entrance scores. In fact, it needs you to go through a psychometric test (in addition to the verbal and quant-based exam) to understand your personality. Next, you go through the Talent Appreciation interview which does not aim at rejecting the candidates but at appreciating them and analyzing their strengths and weaknesses.
Once you go through the entire cycle, your overall fit is decided and you are offered admission.
Hope this helps.