Illinois/indiana Junk yards

No offense, but I think you might be about 30 years late asking this question, particularly for a 36 Cad.

there's still a few oldies yards - there is a 37 or 38 Buick ambulance, a 41 Buick Special, and some pre-war Fords in one I've "shopped" at

At least one '36 3-window on eBay right now. Might be easier to find the Caddy parts there, too. 30s cars no longer grow out of the trees in salvage yards.