Hmm. I hope SI isn't somehow obligated to use one of the designs submitted, if none of them are good enough, or if, as you suggest, there is a best design which could be improved. Presumably the winning designer could be asked to do further work; but what about e.g. SI hiring an artist to improve the winning design?
Also, good point about the 'the'. I'd better make a 'The Singularity Institute' logo too, just in case. (The closest thing to a logo they have on their website now has a 'the'.)
Maybe just knowing there is such an image will help me think of it. Or maybe it will inspire me to attempt to duplicate your exploit.
If you have graphic design experience, check out the on-going logo design competition at 99designs for the Singularity Institute. There are still 6 days left to enter and be eligible to win the $295 prize if your design is selected. Tell your friends with graphic design experience too. There are very few submissions currently.
Note: This is a blind contest. Designers can only see their own entries. All designs will be revealed when the contest ends.
If you're interested at getting a peek at the designs, they will be online after the competition is over. This is standard practice in 99designs contests to prevent designers from contaminating each other and having all the designs drift in a certain direction.