The timeline with Cullen's departure and the spread of Red Lyrium is unclear, yes. But the city guard had been toothless for a long time in comparison to the Templars, against Reds they would stand even less of a chance. Under Meredith's reign there were multiple large-scale conspiracies that neither her nor Cullen knew about, apparently. So, for the Gallows that's just business as usual.
It's not about supporting Orsino, it's about stirring the pot, delivering a much-needed shock to the broken Circle system that people can't ignore, as opposed to propping it up for the sake of expedience and pretending everything is fine.
There is no confusion, Hawke left before Cassandra's arrival. Cullen left with her.
Against a large force? Yes, but if they were a small force they could have handled it. And it was a small conspiracy, not a large one capable of threatening the Viscount. I get you dont like the templars in Kirkwall, but it doesnt make what happened good writing.
And in doing it you were supporting the abominations, blood mages and that madman. No thanks.
We already have that discussion, you think the templars were worse than the mages and I think the contrary, lets just move on now.