Work pin for pin. Start in one corner, next pin is the diagonal opposite pin. (That is, to get head spreaded).
Like:
01-03-05-07-09-11-13-15
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16-14-12-10-08-06-04-02
Put MORE SOLDER on the pin.
Use thick solder wick, wet by flux.
Put enough flux on the big solder blob.
That works for me in most cases. You need (especially with lead free solder) an certain amount of solder to start the flow and spread the heat. If its to less solder, there is no way for the heat, to reach all surfaces, and the surface tension is holding the solder back and is still stronger than the capillary suction of the solder wick!
It sounds weird, but that is physics!
Let the board cool down every 4 or 6 pins.