Funny you mention that. I was having leaks too with the build as it was written. I just kept tightening it down as much as I could and finally got it there...took some work, but it's rock solid now.
I was able to get rid of the leaks with just 4 washers, but i was not able to open close the ball valve without cringing at the feeling it gave me that it was going move too much without eventually springing a leak.
After I filled the cooler to the top with water and f'ing around enough with the valve, leak it did.
Took everything apart and started to measure everything with a measuring tape and came to the conclusion that my cooler could probably be a bit different and the wall where the spigot was located was a bit thinner than the one used in the OP's post, either by fabrications variations or just a plain different model altogether.
So I added the extra washers, for a total of 6 and 2 orings on the outside and it became rock solid, and no more leaks.