i leave food/water out for Moses too. i just leave pee pads in his area & when he has to go, he just gets up and goes on his own. looks like he goes about twice a night. he's on a schedule to potty outside first thing in the morning when i wake up though. He has a potty schedule during the day, but at night or whenever he's in his gated area he knows to use the pad.
I think you could just train your baby to go on pad at night if they're in a closed off area. That way you can get some rest! HTH!