I’m not sure if I understand the question, but I would make 4 boxes and join them with a single plywood back and forget the bottom rail. Then use euro hinges. Maybe push the legs in to hide them. Might be too “modern” than what you’re going for aesthetically, but it’s simple to build. The entire “look” then comes down to how you style the top and the doors. It takes the face frame out of the equation and simplifies things a lot. Anyway, something to think about.
If I hijacked your design, sorry in advance!
Losing fingers since 1969