I do not like the Moby much at all. However the one thing I do like is that it is versatile. Try wrapping your baby in different ways to nurse. I was able to nurse a little better holding mine in a more upright carry. The biggest problem I had with that was he tended to sink because of the stretch in the material and I ended up having to hold him in position after awhile. I don't have that problem with a woven wrap or the Ergo. Since you already have the Moby, I would poke around and find some different holds and just try them out to see how your baby does.
In my experience, NIP is more difficult with a cover and I've only really ever used mine for pumping. However, I've seen lots of mamas around here using them pretty effortlessly so it probably just depends on you and your child. Give it a try and see how it goes.