A sample data set would probably be useful to get more specific suggestions. That said, what you have here is a basic contour plot: several curves that show the relationship between y and x at different, constant values of z.
A lot of charting questions like this tend to end up being more about building the table in the spreadsheet rather than how to plot the data. If you build a good table in the spreadsheet, then plotting the contour plot is relatively easy. If the data layout is poor, then building the chart is difficult. It isn't the only way, but the easiest layout for building a contour plot could look something like this (comma delimited):
If I understand your post correctly, it seems to me that the real question behind your post boils down to how to go from the few data points that you have to the table I describe above. This should be relatively easy if you already know the relationship y=f(x,z), because you simply build the formula into the table and then plot the data in that table. If you don't know f(x,z), then this really become a question about getting that relationship, and, at this point, I'm not sure what to tell you. Perhaps it ends up being a curve fitting problem, but it is hard to know without more information about the problem.
I used this method to create the log grid, but due to reasons, I can't use macros, so I can't relabel the axes. Any other ways? Or would it just be simpler to edit them in GIMP?
GIMP is a photo/image editing software, isn't it? I would think that the easiest options for obtaining the "flexible log scale" effect described in the link would be to use a more robust graphing package than what is built into Excel. Image editor could certainly do it, but I would expect that most graphing packages have built in options for creating the "flexible log scale" effect.
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