I don't know yet about the electrical box because we haven't removed
the old oven yet (they're coming Monday). The only thing with what you
say is that we wouldn't be able to put another oven in the lower part
of the cabinet, which we may want to do. I would assume that there are
only post supports in the back in the diagram so you don't block the
use of the lower part of the cabinet?

Currently there is a double oven that sits on a shelf (which is the top
of a drawer located under the current oven. Wouldn't that imply that a
shelf screwed into the sides would be enough to support a single oven?
(I assume there is some sort of framing around the cabinet, but its
under a fancy veneer and I don't want to risk damaging it)

One thing of note: The cabinet is in the corner, so the back of the
cabinet is not flush against the wall. So wall studs will not be able
to be used. I think there is a bit of space behind the cabinet.