Shubham, sorry to disappoint you but irrespective of all the external factors, what matters and only that matters  is your NEET score and rank in the Merit list. NEET Counselling is  a transparent process. The seats are allotted based on your preferences and NEET score. So to be honest with you, if you belong to General Category, 440 can get you only a seat in a Private Medical College. If it is a Direct Admission for Management Quota, yes what you said might work but if the admission is through State Counselling, the fee structure cannot be tampered. You have to take the DD for the pre settled amount mentioned by the College. Cut offs do not change no matter what the circumstances might be or the relations might be.