Blogger Kenneth DeVries wrote about this in 2011, stating he had solved the mystery. His discussion mentions that many of the other suggestions he'd heard didn't work because of height and other design differences. He proposed the best match was a Muntz Jet (made by the Muntz Car Company in the 1950s), concluding that "the overall form and distinctive front end indicate the car was based on a Muntz Jet."
In 2014 he added a note that various people had pointed him to a "1952 Spohn Palos," made by Spohn Coachworks, a German company that specialized in custom-made cars. DeVries still holds to his "crudely customized Muntz" idea as most probable, though admits the Spohn does have similarities.