Seems like you could probably use this strategy and get rid of the limits by turning this into an extension that would tack on the site list to the search directly(though, I'm unsure if there are such limits directly via the search box on Google or whomever).
I'd also, just from a code quality perspective, bust the list out into it's own property (which could later become smarter), and build the query string out at runtime.
If you need three iterators, it's time for at least one function encapsulating that inner loop.