Our 90s dishwasher died this week and we want to replace it with a true vintage dishwasher if possible, but I've been having a tough time finding one within reasonable driving distance from SC.
You may have to compromise with a KitchenAid from the mid '60s to late '70s. They are the easiest to find because they were built to last. The oldest model that would offer similar capacity to a modern day machine would be the KD-15 series. I think any KitchenAid from the 15 series through the 18 series would be compatible with an original midcentury kitchen.
Here is a KDS-15 (top of the line Superba model)
And here are (L-R) a KDS 17 (series 16 would look the same), KDS-18, and KDS-20
Generally speaking, the models down the line from the Superba will have a visible timer knob to start the machine in addition to buttons for cycle choices and optional functions, something like this: