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I suggest you try the following. Set your two plots in the Question to p1 and p2. Then, col = Map[ColorData["TemperatureMap"][#] &, Rescale[var[[2]], {0, maxvar}]]; ans = MapIndexed[(#1 /. (RGBColor[__] -> col[[Last[#2]]])) &, p1 // InputForm, {6}]; ans[[1]] reproduces p2 without calling GraphPlot3D, which should be faster. This process can, ...

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