I hate these kinds of connections. If it were a pot, it'd go:
Non removable nut part of the bulkhead
O-ring
cooler wall
washer (so that the next nut can tighten without scraping
nut
The o-ring in this spot lets some liquid escape from the cooler but immediately be stopped form going anywhere else afterwards. Fingers crossed you dont' have a leak between the 2 walls of the cooler, the inner white and outer orange or yellow, or liquid will get in between those 2 layers.
The problem with the o-ring on the inside of it, is that while the o-ring will prevent leaks from outside of the o-ring, it won't prevent what comes through under it, closer tot he actual pipe, under the washer and such. Or the threads for the nut that goes next.
My solution was to open up the outer layer of the cooler, the colored portion, being sure that the inner white part stayed intact and untouched. Then the order described above. No more leaks. If your washer is oversized it can then lend some strength to the whole thing so you aren't relying on a flimsy thin wall.
Hope that made sense. Hard to describe. In the first picture, if your wall goes between the O-ring and washer, you won't have any external leaks. Good luck with leaks in between walls though. And assuming that funny ledge isn't so wide that the o-ring can't actually get compressed to start with.