Well, baking won't resolve this one, as even using PT doesn't change it. This is all reflection as far as I can see, so no render settings to change that.
I doubt anything would ever be moving THIS slowly in a final animation though :) And if it is the results will depend very much on what is going on - this is actually all reflectivity, as far as I can see, and is related to the angles of the lights in this particular scene and how much they change with the small movements; could also be related to bloom and glare too (either making it worse here, or it could also be that careful use of bloom and glare could soften that out). It may also be related to the super high Fresnel IOR. Potentially, some softening of the reflections with Glossiness might help. Could also check into Blur/Sharpen as well. So, lots of things to try to soften out how those reflections are changing from frame to frame, should you find yourself looking for something moving this slowly in the future!