plotting – Log scale for ListContourPlot when the axes have different orders of magnitude


I am trying to plot a data set (download here) in Mathematica (it’s 3.9 MB and I wasn’t sure how to best share it) which I then want to visualize with ListContourPlot. Note: the exact data is not really relevant to this question as I am less concerned about what the plot looks like and more interested in the tick marks on the vertical axis and the scale in the legend.

If I naively try a ListContourPlot, I get this image:

NTable=Import()//ToExpression;
data = Flatten(NTable, 1);
plot0 = ListContourPlot(data)

enter image description here

However, I can get Mathematica to interpret this data set using Charting`FindTicks from this question.

data = Flatten(NTable, 1);
trdata = Transpose(data);
ranges = Through({Min, Max}(#)) & /@ Most@trdata;
plotdata = Transpose@MapAt(Rescale, trdata, {{1}, {2}});
plot1 = ListContourPlot(plotdata, 
  FrameTicks -> ({#, 
       None} & /@ (Charting`FindTicks({0, 1}, {##})(0, 1) & @@@ 
       Reverse@ranges)), FrameTicksStyle -> 15, 
  PlotLegends -> 
   BarLegend(Automatic, LegendMarkerSize -> 180, 
    LegendFunction -> "Frame", LegendMargins -> 5))

enter image description here

This is a start, though I still want the vertical axis and the legend to be a log scale. Adapting the methodology in this question (I have Mathematica 11.2), I get

plot2 = ListContourPlot(data, 
  ScalingFunctions -> {Automatic, "Log10", "Log10"}, Mesh -> None, 
  PlotRange -> All, 
  PlotLegends -> 
   BarLegend(Automatic, LegendMarkerSize -> 180, 
    LegendFunction -> "Frame", LegendMargins -> 5))

enter image description here

I get my log scale on the vertical axis, but not in the legend. But more importantly, Mathematica isn’t plotting all the data points. If I try to combine the two methods, I get:

plot3 = ListContourPlot(data, 
  FrameTicks -> ({#, 
       None} & /@ (Charting`FindTicks({0, 1}, {##})(0, 1) & @@@ 
       Reverse@ranges)), 
  ScalingFunctions -> {Automatic, "Log10", "Log10"}, 
  FrameTicksStyle -> 15, 
  PlotLegends -> 
   BarLegend(Automatic, LegendMarkerSize -> 180, 
    LegendFunction -> "Frame", LegendMargins -> 5))

enter image description here

Now, I am missing most of my tick marks in addition to the data points. What I want is to reproduce the second image, so that my horizontal scale is the same, my vertical scale is ${1,10,10^2,10^3,10^4,10^5,10^6}$ and my legend reads something like ${10^6,5times10^6,10^7,5times10^7,10^8,5times10^8,10^9,5times10^9,10^{10}}$.

I have absolutely no idea how to go about doing this. I have a feeling that I can get around this problem using suitable parameters in Charting`FindTicks (similar to this question), but I do not know how to do this.