I remember reading how to do so in the focus tree, it says you need to be unstable and have enough monarchist support, although I had the problem that I couldn't build up any monarchist support until after Ataturk died, and even then there wasn't enough time to build up enough support. Honestly, it seems like it's excessively difficult to get any part that isn't Ismet Inonu.

Its not very difficult at all. You need to choose focuses and political decision that makes autoritarism popularity lower, lower stability by the decision (for example raids, ban parties) and you need to wait 10 november 1938. Then just wait. Do not choose focus "Honest Elections" and arrest communist leader by the event.