How to make a SMALL video from single still image + audio, one key frame and all the rest p frames or whatever
There are a couple of things which you may still tune in the x264 encoder like listed here but also in the mp3 decoder like shown here if you are OK with a lower audio bitrate.My assumption is that not everything is eaten up by the video.
I have tried
ffmpeg -loop 1 -y -i image.jpg -i audio.ogg -shortest -acodec mp3 -qscale:a 7 -vcodec libx264 -preset ultrafast -tune stillimage -maxrate 5K -bufsize 100K -crf 25  -pix_fmt yuv420p -g 100000 result5.mp4

and got a video file that was half the size of the ogg file.
Here is what the parameters do and how to use them:
-maxrate 5K -bufsize 100K
this has a direct impact on the video bitrate. I lowered the values until I got VBV underflow messages then raised it back again. The quality of the jpeg was very low but got better when I increased bufsize.
-qscale:a 7
This produces a 100 kbit Audio stream which was more than OK for my sample.
In a nutshell, you may need to tweak these parameters a little bit in order to improve things. I suspect that it is actually the audio in your case consuming a large part.
Let me know if it works.