Thanks everyone! These ideas are great, I will try the water, foil, and maybe the canopy.
Unfortunately the nursery door doesn't and will never be able to close fully - we asked a carpenter and even a new door won't fix it, so the cat will always be able to go in there at night. It is a weird design and hard to explain why it can't close.
Don't worry Hollywood about the cat going out at night - we live in an apartment block so when he goes "out" it's actually to an enclosed courtyard on the first floor where his litter is but he can't actually get out to street level and catch any wildlife or get into fights. Hope that puts your mind at ease!
And I will also try not to worry about it but he is nearly 7kg and I have horrible visions of him accidentally suffocating a baby because all he wants to do is cuddle. Also he can jump really high so he would be in a bassinet in one leap.