I haven't done the specific swap you are, but I've had four different transmissions in my truck over time........I haven't had to use a different cross member with any of them.
There are several sets of holes & slots in the middle of the cross member, for the rear mount; & the cross member is reversible in the frame. There are also two different positions drilled for it in the frame rails.
There was one swap (I don't remember which trans now) where I drilled two new holes in the cross member, for the rear mount bolts..........otherwise it has been just 'shift & shuffle'.