I feel thoroughly vindicated. I remember endless arguments with my family (probably not very many at all, actually, but when you're young everything seems endless) when we'd have family sing-songs which would at some point involve singing What shall we do with a drunken sailor (goodness knows why, may have had something to do with my stepdad having been in the merchant navy) and whenever we got to the line "early in the morning" they'd pronounce it to rhyme with...well, "pearl eye," and I'd point out that "early" actually rhymes with "Shirley," so why were they mispronouncing it? And in that sort of tone and attitude that's supposed to shut up inquisitive youngsters everywhere but never does, they'd fob me off with something along the lines of, "that's just the way it is, deal with it," (but not those exact words, obv.).
Then this morning, totally randomly I decided to look up the song's entry on Wikipedia and it looks like I was right, 'cos apart from a couple of sources in the 1950s and 1960s there's no evidence to suggest any weird, unusual pronounciation for "early".
Which I think means, with a 30+ year delay, that I win. Yay!