It may help you quite a bit to realize that some linear algebra shows that all solutions are of the form:
x+y xz xy+z
x2y+z x x+2yz
x+yz x+z xy
By rotating and reflecting we can make the largest corner be x+y, and we can insist that xz > x2y+z. In this case we have 0 < z < y The condition that all values be in the range 1..26 is satisfied if 1 <= x2y+z < x+2yz <= 26. Uniqueness is satisfied if 2z != y.
We can actually make a stronger statement. If 2z < y, then the elements fall in the order x2y+z, xy, xy+z, xz, x, x+z, x+yz, x+y, x+2yz and if y < 2z then the elements fall in the order x2y+z, xy, xz, xy+z, x, x+yz, x+z x+y, x+2yz.
With this many conditions, it should not be hard to enumerate the magic squares up to symmetry. And with some cleverness, I believe you don't even have to enumerate them all.
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