has anyone developed a technical method to take advantage of any unique, supra-computational properties of human intelligence?
A prerequisite for that would be that human intelligence actually has some supra-computational properties, no? Frankly, the more I view human behavior, the more we appear to me to be automatons. But perhaps the recent political climate has left me overly cynical. :)
Of course, human intelligence is better than the current algorithmic state of the art for many tasks. For a practical application of that, you could look at, say, Mechanical Turk.
On the theoretical side, there are people (including some who happen to be computer scientists) who have advanced philosophical arguments for human supra-computational abilities. You could look at, for example, the work of Selmer Bringsjord. You could also do a search on the term hypercomputation, but I suspect you will find that the parts which fall under the domain of TCS have nothing to do with people, and the parts that attempt to deal with human intelligence have little to do with TCS (or science in general).