How to convert .avi video that has 1 static image in the video (with sound) to mp4 video with ffmpeg to least possible size?

Question

I've an .avi video (divx) that's at 25fps and it has mp3 audio at 64kbit/s. This video has just one image throughout the entire video.

I'm trying to convert this video to mp4 but to make it as small as possible (as there is just 1 frame really!)

I'm currently trying this:

ffmpeg -i video.avi -vcodec libx264 -acodec aac \
-ar 32000 -ab 64k -ac 2 -strict -2 -y video.mp4

But this makes an mp4 video that's similar size to .avi.

Next I tried changing frame-rate to 1fps:

ffmpeg -i video.avi -vcodec libx264 -acodec aac \
-ar 32000 -ab 64k -ac 2 -strict -2 -y -r 1 video.mp4

This made the video file much smaller (10x smaller) but it has an issue that the key-frame doesn't appear at 1st frame of the video. So the only frame in the video appears like 8 or 10 seconds in the video (!).

It looks like the problem here is that ffmpeg keeps dropping frames from video.avi and it doesn't write them to video.mp4 as keyframes. When it does write a keyframe it's late in the video.

It tried using -force_key_frames argument but that didn't help either. I did -force_key_frames 0 and -force_key_frames 1.

Does anyone know how I could create a really small mp4 video with just 1 static frame?