The other thing is if you use pockets, for the bags that are getting stowed in the gut of the plain, then don't pack them stuffed - lay the boosters out flat sep to the nappy, and lay the nappy out flat (like you were using it as a pattern flat on a table) - takes up less room that way.
Another option is to roll them, the inserts, then the nappies - not sure which one would work better
ditto what Emma said re phone ahead and ask exactly what your baggage allowances are.
Also nappies are not heavy (clean ones that is
) so that will work in your favour.
The other thought is they don't ALL (for the bags that go in the cargo hold) have to be in ONE bag - ie you could pack them last (on top when you open the bag) in a few bags - since you won't be 'looking' for them while actually on the plane, and then just 'regroup' them when you get where you're going.
The other thing is then when you DO get there - doesn't matter which bag you open first your nappies are right there