vponomarenko

You might be interested in http://oeis.org/A007341
They give Maple code that computes 1x1, 2x2, up to 20x20, all in under a second.  Doesn't track symmetries, though.

I would have preferred to comment on your blog post, or send an email, but I can't figure out how to do either of those.
-Vadim Ponomarenko