Yeah, the back is a bit too high...and...the radiused wheel openings like it shows in the picture only exaggerates to look of it being too high in the back.
As for the tires, back in those days kits seemed to typically come with almost whatever tire they had recently mass produced more than something specific to the model. There were a few exceptions, like slicks for some of the dragsters, but even those seemed to be the same from kit-to-kit.
From what I found, the Salt Shaker was issued only in ~1977/78. The '37 Chevy with the blanked-out grille dates back to the late 60's. AMT Kits After the Trophy Series
I wonder if this is why we've never seen the Salt Shaker reissued:
Oh well...Maybe someday I'll build my '37 Chevy coupe into a salt flat car...or maybe a gasser, or maybe a custom, or...
Later,