Ae scripting has no access to custom effect controls. It looks like both the file picker and the multi-level dropdowns in your screenshots are such custom effect controls.
Honestly, it is very unlikely that such a feature will come in the future. It would require to change the third party plugins and Adobe's scripting API and Automation Blocks itself.
So you can set the effect properties which are simple dropdown lists or layer choice drop downs, but not those more advanced UI elements, which are fully controlled by the plugins themselves and to whose detailes neither Ae itself nor the scripting API have access to.
I am sorry that I have no better news here...