I went to look at the '27 radiator...
The '27 radiator appears to be wider and taller that the '28 radiator, and the bottom tank is shaped much differently than that of the '28.
On the '27, the lower tank has a hole, to provide for the crank.
It occurs to me, the cross-member must be different, as the radiator must ride a couple of inches lower in the '27 than it does in a '28, or the '27 radiator mounts ahead or behind the cross-member, more likely, behind.
I hope this helps... Or others can contribute their experience...