A lot of people use wool overnight as its far more breathable than PUL and easier to fit over bulky night nappies. You could try a Minki wrap, I've never used one but their pocket nappies are huge so I think their XL wrap will probably fit well. Or maybe an XL WeeNotions?
I've been using XL airflow wraps on Samuel's night nappies. They are ultra-reliable and cover everything, and he's 4. We're in the process of converting to wool though, but we only have 1 pair of shorties at the moment. Can't wait for his custom Kaypee thomas the tank engine longies to arrive