I don't have to sell reality, you need to figure out how to sell fantasy.
First, drop that timeline, the homo thing is new (relatively), Hoover, the FBI, the American Intelligence Community did not go through most of the 20th century fighting a non-existent acusation of homosexuality.
Here is a quick description to steer you into doing your own search. This liberal, but respected historian is harsher on Hoover than I think appropriate, but it gets you started nonetheless.
Liberal Author Crushes NPR Host's Hope to Spread Movie Myth of Gay J. Edgar Hoover
Sorry, the link did not take.
First, drop that timeline, the homo thing is new (relatively), .....
Well, no, I would disagree, given the dates. From your linked source (thanks again):
WEINER: This is a myth. It's been around since 1937, since Hoover went after homosexuals and government. It was - gasoline was poured on the embers of this by Bill Donovan, Hoover's mortal enemy in government. It's been around forever.
So there is a vintage to it, and granting that it's been meat for strong politico-bureaucratic rivals and may be prisoner to various agendas (not least NPR's), still I don't think either Weiner or you can wave it off quite so casually. Conceded marker No. 2 is that homosexuals, when attacked, almost reflexively, and inevitably, countercharge the accuser with homosexuality of his own, to muddy the waters and blackguard their accuser.
IMHO it's time to get busy digging in the Nixon and Johnson presidential tapes. This subject will have come up again.
I'm also acutely interested in Hoover's and LBJ's strong relationship, and how it was that LBJ blackmailed his way onto the 1960 ticket, for the sake seemingly of an office famously reviled only 20 years before by another Texan, John Nance Garner, only to have the Presidency fall into his hands the way it did. But that's another subject that needs deep research.