I believe Swedish Steve may have stumbled on the answer.
If the fuel flow through the FOHE became more & more partially blocked throughout this long cold flt,then a continuous descent at low pwr would not have changed anything, until more fuel was required at engine spool up at 1000ft. Then the ice would be sucked further into the FOHE causing a blockage, it would have melted with time but time was not what they had.
This in fact could explain the cavitation damage of the pumps, it had been happening to a lesser scale on other flts but the temporary "hicups" had not been noticed.
This had been a long very cold flt, with maybe a marginal fuel spec.