"Fair point! All the other data, including the 'burst frequency offset' doppler readings, have been made upon assumptions about speed though ... As they based the model curve on readings from known flights, they must think they know what speed MH370 was doing between pings."
It's more direction than speed though from the Doppler. There will be a frequency shift related to whether the aircraft is travelling one way or the other along the arc (and bear in mind it might be travelling along the arc, at an angle to the arc etc). The size of the frequency shift will depend on speed along the arc but this will be more difficult to determine. Bear in mind that it took two weeks to even extract the directional data as the data collection isn't designed to do that.
Again, if the plane was travelling 10 miles a minute south on the arc and 2 miles a minute west (a fairly shallow angle), I don't know if, even if the data was perfect, it would be possible to distinguish that from travelling 10 miles a minute south and 10 miles a minute west, which is obviously a 45 degree angle to the arc and gives a much greater absolute speed.