Just wondering if given a HAR file can you generate an approximation to speed index without any screen shots. If not, can you please help me understand how can I communicate the essence of speed index to someone not using WPT?
No, the speed index is a visual measurement and the HAR spec and files only provide network request data. If you have a Chrome/Safari dev tools timeline then it can be calculated from that (the timeline has paint information).
The clearest explanation I have heard so far that accurately represents it is that the speed index is the average time of the rendering of the above-the-fold content.