For some reason that makes zero sense... the 370 has two different size emblems. The one in the front is the same as on the 350s but the one on the rear is slightly smaller and because they are recessed, the front size won't fit in the rear.
You're going to have to wait until somebody starts making a rear specific emblem to ditch the chrome hamburger on the back.

I'm not sure which makes no sense to you, that the two emblems are different sizes or that I want the new 370's Z and not the 350's Z?