MediaLive - crop an .mp4 video to only show center punch 9x16?

The current answer is: use MediaConvert to process your mp4 into a cropped, center-cut mp4 of the specified dimensions.

AWS MediaConvert has input cropping and positioning capabilities. Since your source is a VOD, we suggest using MediaConvert to perform the center cut and output a new mp4 which you can then take into a MediaLive channel configured for the output sizes you desire. Refer to the documentation here for output canvas size and positioning:
https://docs.aws.amazon.com/mediaconvert/latest/ug/video-scaling.html#:~:text=If%20you%20choose%20Default%20(Fit,dimensions%20of%20your%20output%20resolution.

MediaLive can scale or stretch input video, but it cannot do cropping, positioning or center cut of the input video. If you pass in a 1920x1080 source, you will get the entire 1920x1080 image placed onto the output canvas whose dimensions you configure. You have a choice of stretching the input to the new dimensions, or seeing black bars on the edges of the canvas. If you set the MediaLive output canvas to align with the center-cut mp4 produced by MediaConvert, your output should be exactly as you described.