@BOAC at 1st Jun 2014, 23:54 :
I calculate that Inmarsat 3-F1 reached its furthest North latitude at about 19:33 UTC on 7 March.
This site has a table of satellite positions at the "ping" times, and shows the maximum North latitude at 19:41 :
Aqqa on MH370
The site also has large files of satellite position and velocity in Excel or CSV formats. I downloaded one of the Excel files, and previously computed very close to the same velocity (about -82 m/s, i.e., South, at the last "ping").
That would give a maximum Doppler of 400 Hz for an aircraft due North or South of the satellite, but less than 40 Hz at the presumed last position, since that position is almost orthogonal to the satellite groundtrack then.
Here's one explanation of how the satellite data could have been processed:
https://www.siam.org/news/news.php?id=2151
It links to this 31 MB set of slides:
http://www.utdallas.edu/~zweck/MH370_UNM.pdf
Slide 47 shows the ground track of the satellite. It's a teardrop shape rather than a figure 8, due to the very slight eccentricity of the orbit. It also links to the aqqa.org site, so all 3 of these sources are probably by the same person (John Zweck).
For any STK users, here's the AGI page on MH370:
AGI Blog