Considering that Tiger crews were usually experienced veterans and aware of the box design, you would most likely face a Tiger in Mahlzeitstellung. This explains why it was still a threat later in the war.
I would call the 76mm Sherman a tougher opponent though, because the Russian T-34 (even in the 85mm version) lacked pretty much anything that lets your crew perform up to the task.
Tbh: I think giving the Amis a better medium tank in form of a 76mm Sherman upgrade and a Jumbo as a heavy would have been sufficient. Maybe a Hellcat for doctrines.