When I went back the next day I was lucky enough to run across the likely culprit - the beautiful and impressive Pileated Woodpecker! These large birds are about the size of crows, and often create deep oblong holes in trees more than two inches in diameter. This one was a male woodpecker - the red on his head crest covers the top of his head and reaches all the way to the start of his beak. On the females the red stops at the crest. The video's a little wobbly, since I was zooming from quite a distance - even so, you can see the woodpecker give me a suspicious look now and then!
Unlike their possibly extinct relative, the Ivory-billed Woodpecker, which once lived in the dense old-growth forests of Indiana, Pileated Woodpeckers have adapted to smaller patches of secondary growth forest and appear to be doing well. Seeing one is always a treat!