The cross dresser part is unsubstantiated, but not the gay part. His lifelong "close friend" Clyde Tolson sure as hell acted like a life partner. They would go on vacation together. Hoover bequeathed his estate to Tolson. Tolson accepted the flag that draped Hoover's coffin. Tolson is buried a few yards away from Hoover.
Roy Cohn was a source of information about Hoover, and he was definitely credible on that particular subject. Cohn's take was that Hoover was too scared of his sexuality to act on it, but that's still confirming that he was gay or bi. As for the cross-dressing, you're right a lot of the published material relies on an unreliable witness, but Roy Cohn apparently told people about it before it became a topic of public discussion. Now, that's hearsay and unreliable I think, but it's more than just one witness. That said, it is not well established at all.
The homo/bisexuality seems pretty solid, even if there are people who deny it. Another piece of evidence: Lela Rodgers was his beard.