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blokhead
The Siamese method you linked to seems to be only applicable for n x n squares made up of the numbers 1 through n<sup>2</sup>. In this problem you are asked about 3 x 3 magic squares made up of numbers 1 through 26. So there is much less structure and the Siamese method (even augmented as you have done) will likely not find all such squares.
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Unless you happen to fall upon an ingenious simple mathematical simplification, there may be nothing much simpler than trying all possible arrangements of 9 numbers chosen between 1 and 26.
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So I would start the other direction, so that there is less to search. Start with the person's name, say PAUL, and figure out which sets of 5 letters could be added to make a magic square. There are some simple constraints that limit the amount of search, for instance the sum of all the entries should be a multiple of 3. Then see if you can make a magic square out of it. It will be less work than searching the entire space.
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