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This employer, though he is apparently helping his employees, seems to be an impossible type of person. You have to just put up with him. Better try to convince the prospective employer to permit you to join only after actually serving the notice period as insisted by the current employer. Who knows the exact reason - whether it is his trait of stubbornness or the pre-closure operations actually involve your service. If mountain will not come to Mohammet, then Mohammet has to go to the mountain - that's all!
Now you've to decide the course which is situationally appropriate. Your current employer is going to shut down his business on 31-03-2018. Yet he insists on your service until the last date, though you are willing to buy out the remaining part of your notice period to have a formal and peaceful relief so as to join the new employer on the date specified him. Your request to join after 31-03-2018 is categorically turned down by the prospective employer. If you try to satisfy both, any how, you will have no job beyond 31-03-2018. Therefore decide accordingly.