cockpitvisit
"From the 6 pings, there must be 6 different rings. But we are only shown curves from a single ring (probably from the final one). Is there any information about the other 5 pings? It would at least help determine the lateral motion of the plane (how much it moved "towards" or "away" from the satellite)"
Maybe somebody has explained this already but you are absolutely right - we have to assume 'they' only had the transit time for that single last ping - if not there would seemingly be a treasure trove of further information from the other pings. However I think we can rely on 'them' to have extracted every last scrap of useful data.