I used to do a lot of underwater swimming (though never for anywhere near that distance). What I found was that I could cover the most distance on one breath by swimming slowly. This was contrary to my instincts, which told me that the faster I swam, the less time I'd have to go without air, and therefore the better off I'd be. But what I found was that swimming faster reduced the amount of time I could go without air by more than it increased my speed.
I used to do a lot of underwater swimming (though never for anywhere near that distance). What I found was that I could cover the most distance on one breath by swimming slowly. This was contrary to my instincts, which told me that the faster I swam, the less time I'd have to go without air, and therefore the better off I'd be. But what I found was that swimming faster reduced the amount of time I could go without air by more than it increased my speed.