Hi,
What makes you say that you can't use FindObjectOfType inside an Action? you can.
I just made it, it's on the ecosystem: FindGameObjectByType
however, you are going to have a problem to expose the list of types, for this, you might want to use this:
https://bitbucket.org/rotorz/classtypereference-for-unityalso, types are too general and broad, what you want actually, is find by component right? so maybe you should let the dev select a component type, the get that component's type and find it like that.
so I used a string, make sure you run proper tests that the type you want to get is a valid type.
Bye,
Jean