After WWII Kaiser had a 4-door convertible in 1949-40 and Frazer in 1951. The only other US-built 4 door convertible after 1941 was the 1961-67 Lincoln Continental. These are production cars, and not custom-built models.
The last Imperial 4-door convertible was the 1938 Chrysler Imperial, same year as Dodge, DeSoto and Chrysler Royal.. Plymouths last, and only, 4 door convertible was 1939.
Other final year 4 door convertibles - Pontiac (1938), Oldsmobile (1941), Buick (1941), LaSalle (1940), Cadillac (1941), Ford (1939), Mercury (1940), Lincoln-Zephyr (1939), Nash (1933), Studebaker (1939), Packard (1941).