No.
Just no.

"The Greater Good" was something he wrote to Grindelwald, back in his school days. In case you forgot, that's roughly eight decades ago. He disavowed himself from it when he broke with Gellert, or at the very least when he defeated him and turned down any political position. It was not his guiding principle in the second war, nor in the first.

Well, 'Eastern Europe being more progressive than the UK' is, at the very least, not the same as 'the USA being more progressive than the UK'. Only very very similar.

In your place, I'd consider going a somewhat different route - rather than holding hands and preaching tolerance because unicorns, the acceptance of Dark Arts is based on respect for power. If you have it (and can wield it), it doesn't matter where it comes from. If being a werewolf grants you power, great. Doesn't mean I won't kill you when we cross paths during the full moon however.

So why wouldn't they do it any other time? Why is Sirius even at Hogwarts?

 

1. Should Hermione be killed by the troll?
-Definitely.

a. Without Harry would Ron have been confident enough to make fun of her?
-It's never been about confidence with Ron, he is brash and stupid enough to say what he thinks, with no thought of the consequences

b. Would Ron have had any friends?
-Yes, just nothing above superficial friendships.

c. If she hadn't met Harry and Ron on the train would Hermione have been closer to Nevile?
-Maybe, but she's dead.

d. Would any of them have known enough to investigate the Stone?
-No.

2. Should Ginny be killed by the diary, leading to a teenage Voldemort running around?
-Yes, but Tom would've been stopped by Dumbledore right after.

a. Would Hermione (if alive) still try to brew polyjuice potion?
-Yes, she's an overachiever by nature.

b. If not, who (if anyone) would find the Diary after Ginny dumped it in the toilet?
-No one, nobody goes to Murtle's domain.

3. With Remus unavailable who would be the defence professor (assuming that they warrant mentioning)?
-Doesn't matter. They'd be gone anyway.

a. Should the dementors still be sent to Hogwarts without Harry there?
-No.

b. If they are, should they bother the quidditch game (or any of the students) without Harry there?
-No.