Hi
From my experience your best 2 options are to do the following
1) use low melt solder (chip quick) to lower the melting point to the point where it will take 20-30seconds for the solder to set again
Or
2) use a hot air rework station to heat them all up at once ,the hot air is really good at desoldering all sorts of things but can melt plastic very easily so if you use this method to desolder something do it from the other side of the board to avoid meting the plastic and use kapton tape to shield and other sensitive things (eg more plastic or capacitors)
Hopefully this helps
Any questions please ask
Thanks:-)