You could use a parser like esprima or its equivalent from the babeljs ecosystem on the JS source instead and just find the global variable with name `__STATE__` and just eval its init expression. Cheaper, more secure, more direct than actually running the JS.
I actually looked into this (from reading docs, never wrote code) and I wasn't able to find a way to convert the AST for the ObjectExpression into JSON or an actual Javascript object.
What you need is a code generation library that will turn the AST back into JS code once you've identified which part of the syntax tree you're interested in. And that's the code you want to then eval(). Esprima has escodegen for that purpose. I'm not sure what the counterparts are in the babel world. Feel free to shoot me an email with any specifics of where you're getting stuck thinking this through (email should be visible from my profile?), and I'll be glad to help.