Gen, you can try fixing the problem with the log being too open by draping a dark bandana or something over it so that it covers the ends nearly completely. That's not as secure as something solid on all sides but the opening, but it may be good enough that he'll use it. If not, a more secure hide is a good idea, though it doesn't have to be identical to the first. Just be creative and try to think like a bp. By the way, he probably has come out when you're asleep and eventually you'll see him sometimes late at night or early in the morning cruising his cage.