Mesoman.
I'm not doubting the Inmarsat ping reception for a minute. What I'm asking is if there is any way the transmitted signal could be altered to give the impression of movement away from the satellite. One example would be slow immersion in a shallow liquid. The doppler shift of the last broken ping could be due to any number of things, so I'm not considering that one.
I forgot to mention the sonic pings. I'm afraid that I'm classing them as too spurious along with the radar sightings. From what I've read here it seems unlikely that the ULBs expired completely more-or-less on their expiry date, a decaying signal was the prognosis so surely those would still be being heard?