You can tell how high the rot goes by poking it with a screwdriver.
I like the box idea. I might make the box smaller than the cab, like a kitchen cabinet, or I might make it larger, like a stand.
I'd make some scale drawings of what's left and experiment some.
If I really, really wanted it to have a stock appearance, I'd splice the old & the new with solid joints, but it would be tricky because you'd need to make things exactly the same size. In that case there is no reson for the top.
Bob