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Your controller sends digital signals. In the “Advanced” tab, set “Dead Zone” to 0 and check “Map digital to analog”. It won’t be perfect, but it’ll work.
For the rest of us, keeping a copy of x360ce_2.0.2.163.exe in your "PC Gaming Tools" folder is like keeping a Phillips-head screwdriver in your drawer: you may not need it often, but when you do, nothing else will do the job.
Newer versions automatically download controller profiles from the internet. While useful, this often overwrites your custom mappings. Version 2.0.2.163 works entirely locally. You control the x360ce.ini and xinput1_3.dll files manually.