Does the wall need to be cut above the joists? Can the existing wall hang down to the bottom of the bottom joist chord? this would allow you to sandwich the wall below the joists with some channels, and then cut the wall below the channels. The channels would support the wall, joists, etc.
What about a beam above on the floor inside of the wall, supported each end, then some sort of saddle thru the floor to hang the joists why the wall is removed, a new beam put in place, then your shoring beam reomved. Thats if you have enough room to slide in a shoring beam on the second floor...
I think that whoever has the majority of the structure should be EOR. I.E, PEMB engineer is EOR and they need to shop out the foundations...I know there are reasons not for this, but it would add some validity to their designs