Rewrite ListPlot using Graphics while perserving point color?

I have a lot of data points, and I have noticed that plotting using Graphics is usually much quicker than plotting with ListPlot. The problem is I am trying to color the data points based off some conditions, so for ListPlot, what I have written to do this is:

coloredData = Style[{#1, #2}, {#3, #6} /. {{0, 0} -> Gray, {0, 1} -> Black, {1, 0} -> Red}] & @@@ Partition[Flatten@data, 6]
ListPlot[coloredData]

Now, without the Style, if I were plotting my data using Graphics, I do:

dPlot = Table[Point[data[[i, All, {1, 2}]]], {i, Length@data}];

So I wanted to do the same thing with coloredData, and wrote:

cPlot = Table[Point[Partition[coloredData, 20][[i, All, {1, 2}]]], {i, Length@Partition[coloredData, 20]}];

From the error message it seems that now the data is in the wrong format for plotting using Graphics.

So my question is this: how do I rewrite what I currently plot using ListPlot, but with Graphics? When I try looking up phrases such as “coloring points according to conditions” I’m finding results like this and this which use ListPlot, and for computational time concerns, I’d like to use Graphics instead. Any advice for how to tackle this, would be much appreciated!

Here is some of my data:

data = {{{20, 6.48815, 1, 0.876608, 0.5, 0}, {20, 6.47738, 0, 0.521964, 0.5, 0}, {20, 5.97118, 0, 0.0862234, 0.5, 0}, {20, 2.15164, 0, 0.377913,0.5, 0}, {20, 6.43098, 0, 0.0116446, 0.5, 0}, {20, 7.88699, 1, 0.927266, 0.5, 0}, {20, 3.10361, 0, 0.543757, 0.5, 0}, {20, 7.96474, 1, 0.479332, 0.5, 0}, {20, 1.86771, 0, 0.245349, 0.5, 0}, {20, 7.12694, 1, 0.759896, 0.5, 0}, {20, 1.70262, 1, 0.984993, 0.5, 0}, {20, 5.54488, 1, 0.217045, 0.5, 0}, {20, 8.75599, 1, 0.459017, 0.5, 0}, {20, 2.24446, 1, 0.884729, 0.5, 0}, {20, 1.81927, 1, 0.583854, 0.5, 0}, {20, 2.45835, 0, 0.263973, 0.5, 0}, {20, 8.80958, 1, 0.91956, 0.5, 0}, {20, 2.96297, 1, 0.423835, 0.5, 0}, {20, 8.2311, 1, 0.98729, 0.5, 0}, {20, 5.76275, 1, 0.587943, 0.5, 0}}, {{20, 6.48815, 1, 0.876608, 0.5, 0}, {20, 6.47738, 0, 0.521964, 0.5, 0}, {20, 5.97118, 0, 0.0862234, 0.5, 0}, {20, 2.15164, 0, 0.377913, 0.5, 0}, {20, 6.43098, 0, 0.0116446,0.5, 0}, {20, 7.88699, 1, 0.927266, 0.5, 0}, {20, 3.10361, 0, 0.543757, 0.5, 0}, {20, 7.96474, 1, 0.479332, 0.5, 0}, {20, 1.86771, 0, 0.245349, 0.5, 0}, {20, 7.12694, 1, 0.759896, 0.5, 0}, {20, 1.70262, 1, 0.984993, 0.5, 0}, {20, 5.54488, 1, 0.217045, 0.5, 0}, {20, 8.75599, 1, 0.459017, 0.5, 0}, {20, 2.24446, 1, 0.884729, 0.5, 0}, {20, 1.81927, 1, 0.583854, 0.5, 0}, {20, 2.45835, 0, 0.263973, 0.5, 0}, {20, 8.80958, 1, 0.91956, 0.5, 0}, {20, 2.96297, 1, 0.423835, 0.5, 0}, {20, 8.2311, 1, 0.98729, 0.5, 0}, {20, 5.76275, 1, 0.587943, 0.5, 0}}, {{20, 6.48815, 1, 0.876608, 0.5, 0}, {20, 6.47738, 0, 0.521964, 0.5, 0}, {20, 5.97118, 0, 0.0862234, 0.5, 0}, {20, 2.15164, 0, 0.377913, 0.5, 0}, {20, 6.43098, 0, 0.0116446, 0.5, 0}, {20, 7.88699, 1, 0.927266,0.5, 0}, {20, 3.10361, 0, 0.543757, 0.5, 0}, {20, 7.96474, 1, 0.479332, 0.5, 0}, {20, 1.86771, 0, 0.245349, 0.5, 0}, {20, 7.12694, 1, 0.759896, 0.5, 0}, {20, 1.70262, 1, 0.984993, 0.5, 0}, {20, 5.54488, 1, 0.217045, 0.5, 0}, {20, 8.75599, 1, 0.459017, 0.5, 0}, {20, 2.24446, 1, 0.884729, 0.5, 0}, {20, 1.81927, 1, 0.583854, 0.5, 0}, {20, 2.45835, 0, 0.263973, 0.5, 0}, {20, 8.80958, 1, 0.91956, 0.5, 0}, {20, 2.96297, 1, 0.423835, 0.5, 0}, {20, 8.2311, 1, 0.98729, 0.5, 0}, {20, 5.76275, 1, 0.587943, 0.5, 0}}, {{20, 6.48815, 1, 0.876608, 0.5, 0}, {20, 6.47738, 0, 0.521964, 0.5, 0}, {20, 5.97118, 0, 0.0862234, 0.5, 0}, {20, 2.15164, 0, 0.377913, 0.5, 0}, {20, 6.43098, 0, 0.0116446, 0.5, 0}, {20, 7.88699, 1, 0.927266, 0.5, 0}, {20, 3.10361, 0, 0.543757, 0.5, 0}, {20, 7.96474, 1, 0.479332, 0.5, 0}, {20, 1.86771, 0, 0.245349, 0.5, 0}, {20, 7.12694, 1, 0.759896, 0.5, 0}, {20, 1.70262, 1, 0.984993, 0.5, 0}, {20, 5.54488, 1, 0.217045, 0.5, 0}, {20, 8.75599, 1, 0.459017, 0.5, 0}, {20, 2.24446, 1, 0.884729, 0.5, 0}, {20, 1.81927, 1, 0.583854, 0.5, 0}, {20, 2.45835, 0, 0.263973, 0.5, 0}, {20, 8.80958, 1, 0.91956, 0.5, 0}, {20, 2.96297,1, 0.423835, 0.5, 0}, {20, 8.2311, 1, 0.98729, 0.5, 0}, {20, 5.76275, 1, 0.587943, 0.5, 0}}, {{20, 6.48815, 1, 0.876608, 0.5, 0}, {20, 6.47738, 0, 0.521964, 0.5, 0}, {20, 5.97118, 0, 0.0862234,0.5, 0}, {20, 2.15164, 0, 0.377913, 0.5, 0}, {20, 6.43098, 0, 0.0116446, 0.5, 0}, {20, 7.88699, 1, 0.927266, 0.5, 0}, {20, 3.10361, 0, 0.543757, 0.5, 0}, {20, 7.96474, 1, 0.479332, 0.5, 0}, {20, 1.86771, 0, 0.245349, 0.5, 0}, {20, 7.12694, 1, 0.759896, 0.5, 0}, {20, 1.70262, 1, 0.984993, 0.5, 0}, {20, 5.54488, 1, 0.217045, 0.5, 0}, {20, 8.75599, 1, 0.459017, 0.5, 0}, {20, 2.24446, 1, 0.884729, 0.5, 0}, {20, 1.81927, 1, 0.583854, 0.5, 0}, {20, 2.45835, 0, 0.263973, 0.5, 0}, {20, 8.80958, 1, 0.91956, 0.5, 0}, {20, 2.96297, 1, 0.423835, 0.5, 0}, {20, 8.2311, 1, 0.98729, 0.5, 0}, {20, 5.76275, 1, 0.587943, 0.5, 0}}, {{20, 6.48815, 1, 0.876608, 0.5, 0}, {20, 6.47738, 0, 0.521964, 0.5, 0}, {20, 5.97118, 0, 0.0862234, 0.5, 0}, {20, 2.15164, 0, 0.377913,0.5, 0}, {20, 6.43098, 0, 0.0116446, 0.5, 0}, {20, 7.88699, 1, 0.927266, 0.5, 0}, {20, 3.10361, 0, 0.543757, 0.5, 0}, {20, 7.96474, 1, 0.479332, 0.5, 0}, {20, 1.86771, 0, 0.245349, 0.5, 0}, {20, 7.12694, 1, 0.759896, 0.5, 0}, {20, 1.70262, 1, 0.984993, 0.5, 0}, {20, 5.54488, 1, 0.217045, 0.5, 0}, {20, 8.75599, 1, 0.459017, 0.5, 0}, {20, 2.24446, 1, 0.884729, 0.5, 0}, {20, 1.81927, 1, 0.583854, 0.5, 0}, {20, 2.45835, 0, 0.263973, 0.5, 0}, {20, 8.80958, 1, 0.91956, 0.5, 0}, {20, 2.96297, 1, 0.423835, 0.5, 0}, {20, 8.2311, 1, 0.98729, 0.5, 0}, {20, 5.76275, 1, 0.587943, 0.5, 0}}, {{20, 6.48815, 1, 0.876608, 0.5, 0}, {20, 6.47738, 0, 0.521964, 0.5, 0}, {20, 5.97118, 0, 0.0862234, 0.5, 0}, {20, 2.15164, 0, 0.377913, 0.5, 0}, {20, 6.43098, 0, 0.0116446,0.5, 0}, {20, 7.88699, 1, 0.927266, 0.5, 0}, {20, 3.10361, 0, 0.543757, 0.5, 0}, {20, 7.96474, 1, 0.479332, 0.5, 0}, {20, 1.86771, 0, 0.245349, 0.5, 0}, {20, 7.12694, 1, 0.759896, 0.5, 0}, {20, 1.70262, 1, 0.984993, 0.5, 0}, {20, 5.54488, 1, 0.217045, 0.5, 0}, {20, 8.75599, 1, 0.459017, 0.5, 0}, {20, 2.24446, 1, 0.884729, 0.5, 0}, {20, 1.81927, 1, 0.583854, 0.5, 0}, {20, 2.45835, 0, 0.263973, 0.5, 0}, {20, 8.80958, 1, 0.91956, 0.5, 0}, {20, 2.96297, 1, 0.423835, 0.5, 0}, {20, 8.2311, 1, 0.98729, 0.5, 0}, {20, 5.76275, 1, 0.587943, 0.5, 0}}, {{20, 6.48815, 1, 0.876608, 0.5, 0}, {20, 6.47738, 0, 0.521964, 0.5, 0}, {20, 5.97118, 0, 0.0862234, 0.5, 0}, {20, 2.15164, 0, 0.377913, 0.5, 0}, {20, 6.43098, 0, 0.0116446, 0.5, 0}, {20, 7.88699, 1, 0.927266,0.5, 0}, {20, 3.10361, 0, 0.543757, 0.5, 0}, {20, 7.96474, 1, 0.479332, 0.5, 0}, {20, 1.86771, 0, 0.245349, 0.5, 0}, {20, 7.12694, 1, 0.759896, 0.5, 0}, {20, 1.70262, 1, 0.984993, 0.5, 0}, {20, 5.54488, 1, 0.217045, 0.5, 0}, {20, 8.75599, 1, 0.459017, 0.5, 0}, {20, 2.24446, 1, 0.884729, 0.5, 0}, {20, 1.81927, 1, 0.583854, 0.5, 0}, {20, 2.45835, 0, 0.263973, 0.5, 0}, {20, 8.80958, 1, 0.91956, 0.5, 0}, {20, 2.96297, 1, 0.423835, 0.5, 0}, {20, 8.2311, 1, 0.98729, 0.5, 0}, {20, 5.76275, 1, 0.587943, 0.5, 0}}, {{20, 6.48815, 1, 0.876608, 0.5, 0}, {20, 6.47738, 0, 0.521964, 0.5, 0}, {20, 5.97118, 0, 0.0862234, 0.5, 0}, {20, 2.15164, 0, 0.377913, 0.5, 0}, {20, 6.43098, 0, 0.0116446, 0.5, 0}, {20, 7.88699, 1, 0.927266, 0.5, 0}, {20, 3.10361, 0, 0.543757, 0.5, 0}, {20, 7.96474, 1, 0.479332, 0.5, 0}, {20, 1.86771, 0, 0.245349, 0.5, 0}, {20, 7.12694, 1, 0.759896, 0.5, 0}, {20, 1.70262, 1, 0.984993, 0.5, 0}, {20, 5.54488, 1, 0.217045, 0.5, 0}, {20, 8.75599, 1, 0.459017, 0.5, 0}, {20, 2.24446, 1, 0.884729, 0.5, 0}, {20, 1.81927, 1, 0.583854, 0.5, 0}, {20, 2.45835, 0, 0.263973, 0.5, 0}, {20, 8.80958, 1, 0.91956, 0.5, 0}, {20, 2.96297,1, 0.423835, 0.5, 0}, {20, 8.2311, 1, 0.98729, 0.5, 0}, {20, 5.76275, 1, 0.587943, 0.5, 0}}, {{20, 6.48815, 1, 0.876608, 0.5, 0}, {20, 6.47738, 0, 0.521964, 0.5, 0}, {20, 5.97118, 0, 0.0862234,0.5, 0}, {20, 2.15164, 0, 0.377913, 0.5, 0}, {20, 6.43098, 0, 0.0116446, 0.5, 0}, {20, 7.88699, 1, 0.927266, 0.5, 0}, {20, 3.10361, 0, 0.543757, 0.5, 0}, {20, 7.96474, 1, 0.479332, 0.5, 0}, {20, 1.86771, 0, 0.245349, 0.5, 0}, {20, 7.12694, 1, 0.759896, 0.5, 0}, {20, 1.70262, 1, 0.984993, 0.5, 0}, {20, 5.54488, 1, 0.217045, 0.5, 0}, {20, 8.75599, 1, 0.459017, 0.5, 0}, {20, 2.24446, 1, 0.884729, 0.5, 0}, {20, 1.81927, 1, 0.583854, 0.5, 0}, {20, 2.45835, 0, 0.263973, 0.5, 0}, {20, 8.80958, 1, 0.91956, 0.5, 0}, {20, 2.96297, 1, 0.423835, 0.5, 0}, {20, 8.2311, 1, 0.98729, 0.5, 0}, {20, 5.76275, 1, 0.587943, 0.5, 0}}};

newcoloredData = 
  Style[
    Point[{#1, #2}], 
    {#3, #6} /. {{0, 0} -> Gray, {0, 1} -> Black, {1, 0} -> Red}
  ]& @@@ Flatten[data, 1];

Graphics[{coloredData}, Axes -> True]

coloredData2 = 
  Style[
    Point[{#1, #2}], 
    {Gray, Black, Red}[[FromDigits[{#3, #6}, 2] + 1]]
  ]& @@@ Flatten[data, 1];

coloredData2 == newcoloredData         (* Out: True *)

pointListWithVertexColors = Point[#, VertexColors -> #2] & @@ 
    Transpose[coloredData /. Style -> List];

Graphics[pointListWithVertexColors, ImageSize -> Large]

pointListWithVertexColors2 = Point[#, VertexColors -> #2] & @@ 
  Transpose[{{#, #2},  {#3, #6} /.
    {{0, 0} -> Gray, {0, 1} -> Black, {1, 0} -> Red}} & @@@ (Join @@ data)]

pointListWithVertexColors == pointListWithVertexColors2

Graphics[
 GraphicsComplex[
  Flatten[N@data[[All, All, {1, 2}]], 1],
  Point[
   Range@Length@data,
   VertexColors -> Flatten[
     data[[All, All, {3, 6}]] /. {{0, 0} -> Gray, {0, 1} -> Black, {1, 0} -> Red},
     1]]
  ]
 ]