I'll add my 2 cents for what it's worth....
If you were going to feature the minicorps champion at another venue besides I&E, why not let them do an exhibition on Sunday night during that dead time between the last competing corps and retreat? That's got to be at least 15 minutes while all the corps are lining up.
I think this is where you'd have maximum visibility for the minicorps. This is by far the most people that would see them at any one point during the whole weekend. I know the problem would be if the minicorps is a subset of a competing corps, but, typically, that isn't the case.