I'm sure some much more knowledgeable PERLy folks will follow this suggestion with some much more technical ideas, etc. but in the mean-time, the one thing I notice about your data that you're showing, is that they all have a consistent first and last line of each of the data sets.

Could you not utilise that consistency to perform a loop to process each dataset until you either come to the end of the set, or the end of DATA?

In other words, change these two lines:

    next if /Data_Set_\d+: /;
    next if /^NoCoordinateCount/;
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into a couple of loops looking for the start and end of your data set, so you can process each set individually.