This isn't right.
Ray.Direction := Ray.Direction * Index + Normal * (Index * Theta - Phi);
At some point in time, I changed the Index variable to IOR to make it more descriptive. I must have been tired, though, because unfortunately, the code became this instead:
Ray.Direction := Ray.Direction * Index + Normal * (IOR * Theta - Phi);
This compiled because Index was, in fact, renamed too to describe the material object's index (as in its position in the material array). So the refractions were horribly off. How this did not get spotted before is an open question - I only realized it tonight while creating a reference Cornell Box scene and wondering why my sphere wouldn't make nice caustics. This invalidates all of the scenes which include this material (I don't recall when this change occurred, so I have to assume all renders which do not display obviously correct refraction are invalid).
Now to recompute the possibly incorrect renders...