As per agreement it's mentioned that your job can be terminated by management by giving you notice or salary but the clause does not give you option to pay salary and resign as such it's better to send them legal notice.
You need not serve three months notice since the new company can bail you by paying your two months salary to old company. Better send them legal notice stating that you will contemplate legal action and sue for damages if they do not relieve you by accepting resignation letter and payment of two months salary from your side.