Never mind!
I found a way to do what I wanted to do using the Boolean Diff command. I created a solid using those internal surfaces and the Planar command. Then I used the Diff command to subtract that solid from the middle of the larger piece.
I know you can create just about anything with MoI, if you just know the approach you should take.
Mark

Hi Mark, it sounds like you've got it all figured out already - yup if you extrude the outer piece you can then select it and use Boolean difference, selecting the inside wall as the cutting object. That will then divide the extruded object into 2 pieces and you can select the inner core piece and delete it to give you your desired result.

- Michael