I have to go with taking it all out
This setup is not ergonomically correct even for 1956. We used to have a setup like this, but one side of the cooktop was open counter. Even so it was awkward, as there was no space to the right of the cooktop. I would recommend getting appropriate cabinets that are like you have and having a range, that way there is space on both sides for pans and utensils as you cook. I would keep the hood, the pink tile, but a range setup will work much better. Perhaps the old cabinets can be used somewhere else in the house? I would draw something but I don't know how here. I find it's much easier to cook when there is space on both sides of a range.