I'm pretty Schleicher was the one who came up with everything as well as convinced Hindenburg, he was after all a member of the Kamarilla around Hindenburg, and the entire cabinet of Von Papen was selected by Schleicher with basically no input from Von Papen. Their initial alliance was out of an eventual goal to topple democracy, with Von Papen having in mind an ultra-conservative regime and Schleicher having in mind a military dictatorship. Of course, Von Papen had always supported Hinderburg, given that he was extraordinarily conservative, but if Schleicher hadn't brought him up out of nowhere, Hindenburg would not have gotten acquainted with him. You must understand Schleicher's psychology, he wanted to have someone who he can fully control, and that means this person is bribe-able, has no support of his own, whether in public or in the government, and he actually personally knew Von Papen well from their common history in the army. However, while Von Papen remained as expected hopelessly unpopular with the public, he was able to start cultivating a close relationship with Hindenburg, which alarmed Schleicher, so when Von Papen asked Hindenburg to declare martial law, having failed to form a government again and with no hope in sight of ever being able to do so, Schleicher did everything he could to stop that from happening, including rigging a war simulation, that ultimately forced Von Papen to resign. Soon after that, due to some stupid joke Schleicher made about Hindenburg's son, his relationship with the Hindenburgs was rather damaged, and Von Papen had Hindenburg's ear. Von Papen decided to let Hitler become Chancellor while he can stack the cabinet to "hem Hitler in", to achieve a workable government. So Schleicher was kicked out. Had Schleicher still been the sole voice of the army in politics, he could have declared a military dictatorship right then and there regardless of the consequences, but after he kicked out Bruning, many other prominent people in the army started becoming involved in politics, especially with communications with the Nazi Party, so Schleicher could no longer be assured of the complete backing of the army. He was killed a year later in the night of long knives.
Btw, on the topic of Bruning, one of the reasons he was kicked was precisely because he tried to ban the SA, so Hitler promised to Schleicher to cooperate with the next government should Bruning be kicked, and after just a month was forced to resign. Groening, who backed this ban and stood in Schleicher's way upwards, was also kicked with slandering by Schleicher. There are other reason involved in Bruning's removal, such as him being not right-wing enough, Hindenburg's own anger that he was re-elected relying on the votes of socialists and catholics, as well as the general failure of his policies to do much to help the economy.
I have little opinion on Neville Chamberlain, and in fact little interest in British history in general. I guess I'm just into more exciting stuff and trends from history.