i had similar problem with decay and such. i did slightly shorten the new one and put a new one beside the old. i cut off the bottom 2 inches of the bad and added a 2by 2 to fill in ( in this case a old full 2 inch board) then added a 2 by 4 to the other to help hide the cut. the rub is they do make wide like 5 inch hangers with like 3 inch deep throats. this may help you as the beam becomes somewhat wider. shoot i had the whole house up for the new basement block and foundation. i think actual code requires 3 inch bearing.