I don’t know about ALL the screens, might be a little ambitious. Maybe one screen.
If we are talking about even 10fps animation we are still talking about 200 - 300 frames. I think we need to lower our expectations a bit.
On a positive note. If we are going to make the attempt I think that a numbered image sequence might be our best bet, from a graphics development perspective.
The reason I say this is because Photoshop can already load the right format of video as a multi-layer image. Once it’s loaded we can add them to a group and do manipulations and masking on the group, crop the final images as one, and output the layers as a new image sequence.
This, coupled with X and Y position adjustments in the shader, makes it easy to put that video on the screen of the little TV or arcade machine in the background.
(Maybe reusing the same layer in multiple passes would allow us to put the video on more than one screen?)
Using a GIF or even a sprite sheet would require special software that might be beyond reach for a lot of artist.