Is the scripting API source code available?

For instance, if I wanted to make a function that simulated explosion force but scaled inversely instead of linearly, could I take a look at Rigidbody.AddExplosionForce?

No, most of the stuff that the api exposes is just a wrapper to native (c++) code.

it is possible to delve into the reflected api code, but frankly most of it is just bare bones extern functions

No, the API (Application Programming Interface) is just an interface you can use. Unity itself is mostly written in C++ and you can't view the source of the engine itself.