Your desire for leaving the present organization seems to be very intense for the obvious reasons alleged which cannot be found fault with as it's Your right to switch jobs for your betterment.
However, you are bound to abide by the exit clause of your contract of employment. If the acceptance of the buy-out option of the notice period in full or part is subject to the discretion of the employer, you cannot pressurize them to exercise it in a way that suits your own needs. Instead, you could have obtained more time for joining from the prospective employer commensurate with your entire notice period for already you know well about the present employer's attitude. The reason is very simple - always an employer has an upper hand to reject the buy-out option of the exiting employee on the ground of work exigencies. So, it is imperative that the employee should be doubly cautious while switching jobs.
Therefore, my suggestion to you would be to serve the entire notice period patiently without giving any room for complaints and make your separation peaceful and formal. Else you can seek an audience with the CEO of the company and politely convince him to get the formal relaxation.
On the contrary, any decision to walk out on your own by remitting the notice period salary without a formal relieving orders and joining the new job would lead to complications of abscondence, dual employment etc., and would adversely affect all your future career of paid employment.
From India, Salem