You raise some interesting questions. I had not thought much about Huxley's motivation beyond setting promising mids to a task where they would have increased responsibility on a difficult-to-handle ship with fewer hands to man her. He's a wily sea dog who sees more than he lets on, but 75 years away from even a word for queer orientation, would he be able to see two of his crew falling in love? I may be operating under a misapprehension, but I wonder if that wouldn't be as foreign a concept to him as looking in a field and declaring those two stallions are in love with each other? Between the French Revolutionary War and the end of the Regency some 30 years later, there were fewer than 200 executions in the Royal Navy for sodomy, partially because the standards of evidence were so high--- there had to be proof of penetration and of emission(!). Pitt and Blake are always in public locations together and rarely even touch one another. If they ever wander out of the remote regions of the hold with uniforms unbuttoned and hair disheveled, suspicions would erupt, but so far their behavior has been almost pristine.
Phillip Adams is wise to them, but he has inside information so to speak and knows that relationships between men can be considerably more complex than just friendship.
As far as the accommodations in Antigua, Pitt lied to keep Phillip from knowing where Jamie would be billeted, but then Phillip undoes that secret by telling Jamie where he himself was lodging.