I would seriously doubt this is a 1950s American custom car - who would go to the trouble of fabricating a bespoke tubular backbone frame when everyone else was using T or A chassis?
The engine is not from a Trojan (RE or otherwise), although there is a passing similarity to the radiator there are no Trojan components on the vehicle.
The gullwing doors might be a later addition, and hence a red herring, but I'd say it was clear the rest of the car was constructed from scratch in the 1920s or very early '30s as no components are later than this and literally everything is bespoke.
It's a mystery, but it's not unsolvable. If we could find out where the car is now it would be a big help...
