Throw his butt outside!!! He's getting stir-crazy being cooped up. He knows where the food bowls are he's not going to go on an adventure hike the first few times he's out.
We didn't keep the cat inside at all when we first got her, she prefers to do her "business" outside instead of in the litter box.
She learned real quick to be quiet at night if she wants to be in (cold/rainy nights) and on the nice nights she doesn't even come back at bedtime. (Dogs and cat get one last chance around 11pm to come in for the night) Dogs are always in by then and the cat gets to choose.
Duct tape is a good alternative though!!!