I think your idea of trying to get him to eat the food inside is good. Maybe you could start with some food outside the door and then put some more closer to the door and then just inside the door and then inside and then inside the cage maybe. But if you think that is too long for him to spend in there, if the cage is small, maybe you could carry the cage into the bathroom as others have suggested and let him sleep in there tonight. And hopefully you can get him in the cage tomorrow morning without getting too scratched up.

Hope it all works out.

p.s. is there anyone you can borrow a large crate from? That way you could have litter box inside the cage and once you get him in there tonight, you could just leave him in there.