Notice period states 2 months mandatory & 1 month buy out on mgmt discretion but asked to serve full

As per the HR Policy (outdated as per HR and not even updated) and Employment Agreement, it has been clearly stated that 2 months is mandatory to serve and 1 month buy out is applicable on management discretion. My new employer asked me to join on a certain date that fell under the 2 months mandatory notice period. I have put request several times and spoke to each and every member of organisation beat HR head, CEO and Reporting Manager. Reporting Manager accepted the request but the HR and Senior Management is persistent to seeve the notice period of full 3 months. I have proposed a buy out option as per policy and also stated that without pay I will assist in the duties which they feel still need my assistance. Due to lack of decision making and eventually delaying it till my joining date, I have to abscond the services and have to join the new organisation. I was continuously asking the employer that I am ready to payoff the notice period severity damage or abscond me without giving any experience letter just to clear the financial pending that is due with the firm. They are persistently saying its already been decided that I have to serve 3 months mandatory notice period. Please help me with the this. As I joined a new organisation that is giving me both challenging job role and compensation as per market standards and they already said previously if I am unable to join after 2 months notice period then they have to decline my candidature as that was an urgency of the assignment that will be given to me. Its really tormenting and hampering my mental health. Guide me please