Your first two methods, using the RAND function with the GUMBEL distribution and using RAND with the UNIFORM distribution and using an inverse transform on the cumulative density function for the Gumbel, should return results that are very close - if not identical.
The third method, generating observations from the Gumbel using a pre-defined set of probabilities (the values from your DO loop index) will not be considered by most to be a random sample from the Gumbel. That method will give you a very nicely shaped Gumbel curve, but there is no randomness in the selection of your probabilities.
There is a method that was quite popular in years past called Latin Hypercube sampling that might be of interest to you. Suppose you want to generate 100 random values from a distribution. Instead of using the pre-defined probabilities from the the index of a do-loop, generate a probability from each of the 100 equal-width probability intervals that cover the range 0-1. So, generate a probability on the intervals 0-.01, .01-02, ... , .99-1.0. Use those probabilities with the inverse transform on the cumulative density.
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