....I haven't gotten the car over my pit yet, but I assume I can access the radiator from below?
The louvers separate the radiator from the upper grill; but the radiator is always open to the lower grill. However, there is not much of a gap between the radiator and the louvers, so trying to reach in and up through the lower grill would likely be fruitless.
To get access from below, you'd have to remove the front skid plate, which also means removing or loosening the adjoining panels to the left and right of the skid plate as well. Perhaps it would be easier to remove the plastic panels on top, in the engine bay, for access.
If you are able to get the louvers open, avoid sticking your hand through them without first blocking them open with a solid piece of wood or something similar. You don't want to take a chance on the louvers closing while you're working in there. Sorry I don't know how they are actuated, or how to properly lock-em-out. Perhaps someone else here does. Best of luck finding the path of least resistance.