I've tried Rapadura once before. From my recollection, it was much drier than brown sugar and I don't recall having tempering issues because of it. I do recall that it added a noticeable molasses flavor to the batch of chocolate I used it in, so I haven't used it in chocolate since as I'm not looking to try to add flavors from the sugar...yet. Anyway, my wife slowly used up the remainder in baked goods. Tasty!
Another lesser-refined sugar that I have tried and really enjoyed was called Muscabado from the Philippines. Alter Eco (I think) sells it here in the US. It had a noticeable "unrefined" odor to it, not quite molassesy. The package said vanilla and caramel notes. The chocolate that I made with it didn't seem to have an altered tasted because of it though. Note that at that time, I only had one refiner so I made two back-to-back batches of the same cocoa bean origin: one with bulk organic cane sugar and one with Muscabado. Didn't notice any major flavor differences and actually I liked the Muscabado more for that particular origin.
Are you buying the organic C&H from say Costco? I had a negative experience with it in my Santha Spectra 11 refiner. Relative to other organic cane sugars that I had tried before testing the C&H sugar, it had a seemingly much larger particle size. When I put it in my refiner, it was like hearing Pop Rocks going off in my Santha and it definitely dogged the melanger down. Enough so that I was worried it was going to fry my Santha's motor. A heat gun helped though.
Other organic cane sugars that I have tried that had much smaller particle size were from United Natural Foods Inc (UNFI) and Florida Crystals. Both I've ordered 25 lb bags from in bulk from our local natural foods COOP. On sale they were about $30. I know other chocolate makers have mentioned Wholesome Sweetners, but I haven't tried them. Last week, I purchased two 1 lb bags of Muscabado and Wholesome Sweetners sugars to test out and compare to the Florida Crystals I'm currently using. Each 1 lb bag was $3.99 at our COOP, which is pretty pricey but not going to break my bank to test with. I'm sure there's a much larger price break for 25 or 50 lb bags of each, if they sell that large.
Anyway, hope that helps.