The 32-40 has enough taper that it will clear.The problem with converting the .310(without rebarreling)to 32-40 or 32 Win Spec is that the rifling twist is too slow, even though the groove diameter fits better than 32-20.In the 60s, cadets were avaliable converted to 32 Win Spec, but they were not satisfactory with the factory bullet.Of course, a new barrel with correct twist would make a fun rifle, just expensive.
Mike