Solution using ffmpeg:

You can use the select filter in ffmpeg to adjust the order of frames without needing to extract and rename them manually. Unfortunately, ffmpeg doesn't natively support "rotating" frames within a loop in one command, but a workaround can be to duplicate the frames and trim them, so the loop starts at a new point.

Here’s a more streamlined approach:

1. Duplicate the GIF (append the frames of the GIF to itself).
2. Trim the new starting point and cut the GIF down to its original length, ensuring that the loop is still seamless.

The command to do this would look like this:

ffmpeg -i input.gif -filter_complex "[0:v]split[original][copy];[copy]trim=start_frame=X:end_frame=N,setpts=PTS-STARTPTS[part1];[original]trim=start_frame=0:end_frame=X,setpts=PTS-STARTPTS[part2];[part1][part2]concat=n=2:v=1[out]" -map "[out]" output.gif