Fleece is ideal for night use as it allows the moisture to evaporate, so the nappy shouldn't be as wet in the morning.
As fleece isn't waterproof you may find that the outside is very slightly damp in the morning, not wet or leaking, just where the moisture is evaporating.
Natures Babies do a Multiwrap which is a double layer fleece wrap with side snap poppers & let gussets to help with any poo leaks! Or you could get a fleece soaker or flongies (fleece trousers) that he could wear with a t-shirt as pyjamas. Jabula Baby & Bespoke Baby Room stock some lovely ones incl Pumpkinpants.
Hope that Helps!