According to that article about Detroit Electric cars (thanks for the link to kool info) they were supposed to be reviving the brand ~10 years agoIn 1926 you could still buy a new electric car, such as Detroit Electric; they were not much different from the gasoline cars of the time, and you could copy the general design except using modern components (especially the battery and controller).
Swapping in an entire salvaged drive unit, and the independent suspension that is needed to go with it, is usually the technically preferred (but often not at all easy) way to go. In this case, it would be so unlike the original car that it seems like a strange choice.
A variation that might be interesting is the complete drive unit, but with a de Dion axle suspension that would look almost like the original axle at the ends, including the springs if you want. It looks like the original has a plain live beam axle on leaf springs.
A motor (probably with a reduction gear set, depending on motor operating speed range and torque) placed where the original transmission was is still possible, even with a modern motor rather than a brushed DC motor (whether salvaged or new); it would be like the electric cars of the time.
...but, I've never heard of it (or them), did they ever get it going?