This is for the five people in the world with this exact problem …
First, you have an antique three-forths bed and you want to use a standard full sized mattress.
The solution is to create an insert that replaces the box-spring and extends over the side bed rails.
A few years later you need the bed to be a little lower.
The solution is to create a new bed frame with its own legs and inset ends so the antique head board and foot board have something to attach to.
Yeah, like I said, this is for the five people in a world of 7,476,562,882 people who have this problem.