Adding to your excellent idea: Hire the best teachers Hillsdale has to offer to teach the group of kids.
Think of the resource people Both of the Gingrich s. (Karen Pence is a licensed experienced teacher. )
Plenty of museums and national monuments to use as jump off points for history and science lessons. (Writing stimulants).
Math is easily taken care of by computer. Music and art history easily taught with visits to actual paintings and events
Even if not in WH plenty of places a one room base could be located.