Flicker in shadowy areas of animation frames

I’m making an animation of shiny objects, red and white pill capsules tumbling in a swarm. The frames rendered ok. I made an .mp4 with ffmpeg. The result looked great except for a flickering effect in the shadowy areas, where pills were behind other pills. At first I assumed it was over-done lossy compression. Checking the individual frames, I see it’s due to rapidly changing patterns of light on those partially obscured pills. This does not compress well, even at higher bitrates.

It’s not clear if this is due to specular reflections from the front pills cast upon the back pills, or if it’s inadequate path sampling. I tried increasing from 300 samples (or was it 333?) to 600, and also 1400. More samples helped a little bit, but wasn’t solving the problem. Higher sampling, of course, increases render time. The rendered animation already takes 6 days to do as it is.

I’m using Cycles with denoise turned on, using the OptiX denoiser. The camera has aperture 1.5 for depth of focus to soften pills in the distance (outside the snippets shown below.) Using 300 or somewhat more samples for the final work. All procedural textures, no images involved.

I like the overall look and feel of the animation. I don’t want to change anything affecting the lighting or the photorealism. But I need some way to reduce the rapidly varying detail in those shadowy areas with not much cost in render time. What do the fine Blender artists here suggest?

A snippet from four consecutive frames:

(Done with 100 samples, which exaggerates the effect somewhat.)