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I think you could do something like this using the SNES's mosaic parameters. If I recall you can change the "origin" for the mosaic pattern. If you have the mosaic magnitude at 8 pixels (an entire tile taking on just the value of the origin pixel) and shift down the origin every frame, you can represent 8 frames this way. Of course, the "resolution" is cut into 1/8th its original size this way, but the shimmering effect from the position offset is gone.

Remember mosaic works in both axes, so technically an 8 pixel wide mosaic gives you 64 unique origins... May be better to use a less blocky mosaic while keeping a similar amount of frames in a single graphic (and if you combine this with palette trickery the amount of images can potentially explode, e.g. you can store 4 1bpp frames in a single 4bpp image, at the obvious expense of color count).

Memblers wrote:That's a neat idea. I was thinking too, if the animation was only 2 colors, you could squeeze 3 more frames into the same memory.

So you'd have 2 1bpp combined images, then you'd combine them into a 2bpp NES tile arranged like this:
set1: transparent,transparent,color1,color1overlap
set2: transparent,color1,transparent,color1overlap

If that didn't make sense, another way of saying it is

literally having each bitplane be a separate image.

Now, would it be smarter to leave the sprites in place and just update the scroll register? That way your zoetrope-esque image would stay in place.

Scrolling the background would likely pose greater limitations with what you could do (using the sprite overlay). Since most (if not all) sprites would be taken, the background is all you have left to work with if you want anything else on the screen. Unless you do a sprite #0 hit to update the scroll midframe, everything else would be bouncing around.

Unless you did something clever with the blanked lines. You could turn them into prison bars, and have something going on behind them. If this were the case, you'd want the bars to remain in place, and update the scroll.

Yeah, for a moment I thought that having the animation stay in one place might be advantageous...

If you wanted to eliminate the motion, the bars can be made with the background and the animation done with sprites placed underneath. That way you have no choice but to move the sprites.