For a long time I too assumed that Exner and his team were responsible for most of those early-to-mid-1950s show cars, including the Explorer. I got my information mostly from Motor Trend magazine in those days, but no longer have copies that might have dealt with the Explorer.
We now know that Ghia indeed designed as well as built a number of those cars, including the Explorer. His Wikipedia entry credits Ghia owner Luigi Segre (1919-1963) with the design. However, it seems to have been inspired by a previous Ghia product, the Fiat 8V Supersonic whose design is credited to Giovanni Savonuzzi.
The Plymouth Explorer still exists, and you can view it in Los Angeles at the Petersen Automotive Museum. I saw it in the Spring of 2017 and took some photos displayed below.