If Ron Mowrey (Photo Engineer) was still with us, his response to this thread would be, at the very least, interesting!
Despite being one of the named patent holders on the central K-14 Kodachrome patent (assigned to Eastman Kodak by him and his colleague and fellow Kodak employee Richard Bent) he was pretty clear in his opinion that the Kodachrome approach had reached its maximum potential and had been surpassed in quality by the capabilities inherent in the E6 approach.
Any process used to create positive colour film slides or movies needs to include several steps and components.
In essence, E6 films incorporate more of those components in the original film, leaving less to be added or created or modified at the processing stage.
In contrast, the Kodachrome processes move more of those components or steps to the processing stage.
Kodachrome processes were perfect for centralized, very high capacity labs - ideal for the motion picture films that made Kodachrome economically viable. When large numbers of people stopped making home movies using Kodachrome, the processing volumes plummeted, and Kodachrome's future was doomed.
In contrast, the various Ektachrome (and compatible competitor) products were and are well suited to much smaller, lower volume labs.
If someone came up with a process that wasn't E6, and used some of the approaches of the Kodachrome processes, it would be different than any of the Kodachrome processes, it would probably be more complex than any of the Kodachrome processes, and it wouldn't have the advantages of Kodachrome, such as the thin emulsions leading to high potential sharpness.
You would probably have to do something like remove one set of colour image components and then add another, more Kodachrome like set of other colour image components, to make it sufficiently "Kodachrome-like".