If you have not signed any other communication accepting any change in notice period, the notice period and termination clause posted by you shall prevail. Hope you have carefully studied your appointment letter and it is not stated that accepting the notice pay in lieu of notice period shall be subject to approval of the company.
You can submit your notice of resignation under proper acknowledgment, with effective date of resignation, notice period, notice buy out, termination clause as stated in your appointment letter clearly mentioned in it addressed to good offices of your appointing authority/MD/HR Head/company secretary, and request you may be informed in writing with a copy to the designated employee to whom you should submit company property and the designated employee of the company should be asked to handover the proper acknowledgment to you on the spot. You should request that the good offices may arrange and ensure that acknowledgment and acceptance of your notice of your resignation is supplied to you immediately and acceptance your resignation, settlement of you’re a/c and instrument of payment, FNF statement, work experience certificate, relieving letter, from16, PF withdrawal/transfer forms and accumulation reports, NOC/NDC, may be supplied to you …………and you should be informed by a letter that with in which date you shall be supplied all of these.(If you, your elders in the family, competent and experienced well wishers, lawyer/law firm feel it deemed fit you can mention “as per applicable law of the land and corresponding rules/policy of the company” at ………...)
The payment of wages should ideally be effected to the employee within two days from date of separation. Some companies have a policy to supply FNF and payment instrument cheque/DD within a month of date of separation. However peruse and let the company state in writing. You should obtain copy of employee rule book, standing orders of the company and these may be available at the HR page of the intranet of the company or with HR as a hard copy.
You may clear the backlog if any, and complete the tasks on hand. Since your line managers are reluctant you may submit a written communication from your end under acknowledgment with a copy to you, and mention that you have successfully completed all tasks/assignments on hand and have submitted the details to Mr............and all other data/records/details and nothing is pending at your end as on date. You may use your rapport/goodwill and negotiation, persuasion, persistence, reasoning skills to obtain comments in this acknowledgment "that nothing is pending at your end".
If it is workable and you can spare a few days and company is willing to pay you salary, you may agree for a few days. It shall be good professional gesture to help your line managers, HR, company by suggesting good candidates for your replacement and train your replacement.
Even if your next employer is willing to buy out your notice period, you should be nice to your current employer without totally compromising your next employment. It shall be appropriate to study in advance, the notice buy out conditions, offer letter, model appointment letter if you can obtain, and other conditions like service bond if any and seek opinion and advice from your elders in the family, competent and experienced well wishers, lawyer/law firm, before abruptly ending your current employment.
It shall also be appropriate to settle in writing with your next employer that although they are willing to buy out notice period you shall be able to submit the copy of your resignation and receipt issued by post office vide which it is dispatched and POD, you can provide acknowledgment/acceptance of your resignation, work experience certificate, relieving letter, only upon receipt of it from your previous employer as and when it is supplied to you.