What about previous 'ping's
If Inmarsat can establish that the 777 was on a particular arc during the last ping (these are the arcs we have seen recently) they can surely determine the arcs of the previous pings as well. Given that the groundspeed of the plane is probably known to with 10% at worst, a reasonable track of the plane's position should be possible. If it was pinging every half-hour, and we are absolutely certain of its position when the transponder was disconnected, then the range of possible flight paths based on a series of arcs and a estimated speed would be quite small.
I can't imagine why nobody is bringing this up. It's completely obvious.