They already understood each other perfectly.
When Tobirama appointed Hiruzen, at this moment Danzo understood who he was really like Tobirama suggested just before.
Danzo understood that he wasn't fit to be Hokage. That in fact, he was a man of shadow, the one behind the scene. While Hiruzen, the one who instantly uppered his hand, was fit to be the Hokage, the one on the scene.
This is exactly a this moment all started.
Danzo became an Anbu leader, and Hiruzen the Third Hokage.
Danzo was the Root, Hiruzen the Tree.
Fillers episode aren't canon. Danzo never attempted to kill Hiruzen. Danzo knew Hiruzen was fit to be the Hokage and always respected it, while Hiruzen knew Danzo was fit to be in the shadow doing the dirty work.
They perfectly understood each other. Each other understood their role in the village.
Yes, Danzo tried to Become the 5th Hokage. But it was exceptional. Danzo tried to become the 5th Hokage only when he saw after Hiruzen, nobody according his point of view was capable to lead Konoha. He wasn't agree with Hiruzen's policy, but when he saw Tsunade according him was even softer than Hiruzen, in his mind it was " enough is enough ". If a Tobirama-like emerged after Hiruzen death, he would have supported his appoitment instead of talking power himself.
Danzo from Hiruzen era wasn't pretending to become Hokage. He wanted to stay in the shadow.