Y'know, I was thinking about this and realized that what I really want is to have the constraint on both the elbow and the wrist. The wrist doesn't really move around a lot in these situations - the adjustments are through the whole arm. To do that I think I'd need to remove the IK on the arm and just use the joints.

That's fine for my situation because it's just for 20 frames in a very specialized and simple scenario. I can isolate it to a single file and it won't affect any of the other sequences. But how would a person do something like this with a complicated rig in a long, complicated scene?