William Clay Ford, youngest grandson of Henry Ford, was placed in charge of the new Continental project. An initial design by his team was poorly received by company president Henry Ford II and others, so Bill had to come up with Plan B, a design competition. What happened is described by Michael Lamm & Dave Holls in their authoritative book "A Century of Automotive Style," pp. 146-147:
[William Clay Ford, in charge of the Continental project] asked his staff to suggest names of outside stylists, and the groups invited were: George Walker Assoc., consultant to Ford Motor Co.; [Buzz] Grisinger & [Rhys] Miller, independent designers, previously with Chrysler and Kaiser-Frazer; Vince Gardner, formerly with Cord and Loewy; and Henry [Ford] II's brother-in-law, Walter Buhl Ford, who later merged with Harley Earl Assoc.
The Continental project now became a five-way contest. The four outside teams would receive $10,000 each for their Mark II designs, chosen or not. To keep everything fair and consistent, each team had to deliver side- plan- and end-view drawings plus 3/4-front and 3/4-rear perspective sketches. Rules stipulated that all artwork had to be the same size, same matting, use the same supplied perspective grids and be of the same color. No sketches could be signed or identified. Judges -- five executives from Lincoln -- could cast only one vote each and had to pass through the final display area separately so they couldn't talk, nod or read each other's body language.
The final judging took place in Apr. 1953, and the design that ended up winning the competition came from Bill Ford's own Special Products group [the team led by John Reinhart].
One thing to keep in mind is the styling fashion context of the competition and the resulting production car. The Continental Mk. II appeared for 1956, the same year the Studebaker Golden Hawk and the Chrysler Corporation line began sprouting tail fins. Elaborate two-tone paint schemes were found on some 1954 Oldsmobiles and three-tones appeared on 1955 Dodges. Panoramic (wraparound) windshields were found on a few 1953 Oldsmobiles and Cadillacs, then in 1954 all Buicks, Oldsmobiles and Cadillacs had them. Contrasting all this, the Continental was very conservative, having only a moderately wrapped windshield, a single-color paint job and no tail fins. So to some degree the Mark II fit more closely to 1952-53 when it was designed than for its actual model year. On the other hand, even in 1953 its stylists were probably aware of the near-term new concepts and they or management chose to ignore them.
Decent images of the competing designs are hard to find on the Internet, so I had to resort to scanning images from books in my automotive library. The design renderings are from Automobile Quarterly, Vol. 12, No. 1, 1974, pp. 100-101. Side drawings are from "Lincoln & Continental: The Postwar Years" by Paul R. Woudenberg (Motorbooks International, 1980), p. 72. Click on the images to enlarge.
1940 Lincoln Continental Club Coupe
This is the Real McCoy. Future Continental designs had to either speak to it or consciously ignore it (at their peril).
1948 Lincoln Continental Club Coupe - RM Southey's photo
The last Lincoln Continental using original bodywork and facelift features from 1942 and 1946.
1956 Continental Mk. II
The result of the competition and later refinement. Features echoing the original Continental include: a long hood (by the mid-1950s, long trunks were coming into fashion, hoods becoming shorter); somewhat similar passenger greenhouse, including the general shape of aft side windows and the large C-pillar; and the spare tire at the rear (the hump on the trunk lid was atop the actual tire mounted in an angled position beneath it).
I don't think any of the design proposals makes for an appropriate successor to the original Continental. Some details here and there are not bad, but the overall designs are lacking the right stuff. A consistent problem has to do with grilles and front ends in general; most of these designs are bland, characterless. The best of the lot, an opinion I've held for many years, is the second (lower) Grisinger-Miller design. I don't like its front and the little fins at the rear, but the rest of the design comes closest to the spirit (not the details) of the original.
As can be seen in these side views, the designers had very little flexibility in basic layout of the car.