Dear sir,
On careful perusal of conditions explianed in your post, I see another picture and here predict a practical problem with a personal suggestion.You may not possibly loose offer at new organization but certainly you will face difficulty in making over loss of impression unnecessary if situation comes like that. Suggest you to become smart and intelligent and make emotional communication to new employer that the present company is insisting to stay and persuading me by all means tfor completion of all important works within one month's time . As there is no replacement available and the new guy who has been hurriedly selected recently is joining after a month only , so I feel that it is not right to just walk out from a good company leaving my work half done in midway . On this ,you should plead for one month's time to report your joining. You should mention that you would also prefer your graceful exit after completing all pending important assignments in this one month's time and then after a certificate of relieving with proper hand over of charges , you will immediately join. Please make sure that this emotional intelligence is one time formula and its effect is life time.
Best wishes,
RDS Yadav