The targets you need in terms of threat raising are rather rare for CHI if it want to get pushed away from Axis. You would need an Axis member with democratic (blue ideology group) or socialist ruling party (red group). You could try Siam, if they already are Axis and are still ruled by Democrat Party, as well as Romania or Finland if they are already Axis. All of these are unlikely to help early.
As long as JAP and Manchukuo hold so many cores of CHI, there should be a penalty on Axis-drift. As there should be (in smaller amounts) on Allies-Drift for Hong Kong and the French colony in Guangdong. Sometimes onely one of them is shown, sometimes none. Do they have effect even when not shown? I don't know.
Maybe you should forget about the Axis threat and focus on only lowering your neutrality, which should be done most effectively by raising threat on UK. They are of another ideology group, share your land border and have quite an amount of IC. They even hold Chinese cores in Guangdong, but I am not not sure this will have significant impact on their threat to you.
Note that this will to a small amount also help Germany and Italy, but they already are on relatively good laws rather early, so the impact should not be devastating.
Can you list the individual contributions from your diplomatic triangle tooltip?