P&W Kansas city was built to make R-2800s, the R-4360s came later.
I don't believe Wright had a Chicago plant. They did have one in or near Cincinnati. Built a lot of R-2600s before building R-3350s.
The Centaurus first ran in 1938 but it wasn't fully sorted out until 1942.
Bristol had quite a bit of trouble making any of their sleeve valve engines in quantity in 1939-40 making any idea of making said engine/s in a remote location location something of a gamble.