json scriptBrowser Info Environment
You can set the "Company or person" field to "-- Choose whether you're a company or a person --". This way it won't populate that specific json script (as of version 1.1.4, so update if you haven't already). You're then able to paste in some code yourself wherever and whenever you want to. That makes it as customizable as possible I guess!
The word Organization needs to say LocalBusiness. Is there a way to change that?
It reads: "Include a Person or Organization record in your markup with..". So it doesn't say any other value.
If you do want to add your "LocalBusiness", you can add another ld+json section from what I can tell. There's some info here too:
They say "Another element to add to complete your online profile, are links to your social media accounts.". So it seems like both are independent entries, so you can add multiple. Now I'm not the 100% expert here, and it's easy to interpret things different than they're mean to be so.. Correct me if I'm wrong and if you have examples yourself. Always in for improvements and learning something new! :)