Size doesn't matter 16,17,18,20 as long as their rated for the weight and the compound isn't gum they'll take it just fine.
One 17" that springs to mind as perfectly suited upgrade is Pilot Road 2,3,4. Multi compound that is hard down the middle, by hard I mean hard for a sportbike, and soft on the shoulder with vastly superior grip wet or dry to anything offered for the R3. They don't make it our size, but it's an example of a tire that would be a perfect match to R3s.