I agree, you could always put a wrap over the top - fitted with wraps are generally more reliable than pockets/AIOs! You could probably pick up a cheap Mother-ease wrap or something on the classifieds, they're very reliable and not thick/bulky (Airflows are a little poofy but they're still very thin material so wouldn't add a lot of bulk). Or, even better, get some woolies!! Not sure what size you need but there are some lovely and very reasonably priced S/M longies and soakers here
I always thought wool would be too much effort but it really is so easy to care for, and cute too!